More than three months after a dramatic crash in Egypt, the mysterious loss of a Russian airliner continues to generate headlines and controversy. The latest news from Moscow points the finger at international intrigue that seems certain to inflame already incendiary regional tensions. But are these new claims true?

All we know for certain is that Metrojet Flight 9268, an Airbus A321 operated by the Russian airline Kogalymavia, disintegrated 31,000 feet above the Sinai Peninsula on October 31. All aboard, 224 passengers and crew, were killed, and all but five of them were Russians, most of them vacationers headed home after a Red Sea holiday. This catastrophic loss, which spread debris over eight square miles of desert, was the deadliest air disaster ever on Egyptian soil, as well as in the history of modern Russian aviation.

From the outset, Egyptian authorities conducting the investigation into the crash were circumspect as to the cause. While terrorism was certainly possible—something very dramatic happened to Flight 9268 to cause a sudden break-up, without any distress call, at cruise altitude—Cairo was cautious in its public pronouncements, refusing to rule out mechanical problems as the culprit.

In contrast, Moscow almost immediately blamed terrorists for the catastrophe, and the Kremlin has stayed on that message with gusto. Less than three weeks after the crash, Aleksandr Bortnikov, director of Russia’s Federal Security Service, announced that the loss of Flight 9268 was a terrorist act. The FSB, which offered a $50 million reward for information about the perpetrators, concluded that the aircraft was destroyed by two pounds of TNT in a homemade soda-can bomb placed on board. The Kremlin also dropped unsubtle hints that slipshod Egyptian security enabled the disaster.

Mr. Putin seemed embarrassed and angered by the loss of Flight 9268, which cast a pall over his otherwise impressive record of aggressively fighting terrorism against Russians.

Mr. Bortnikov soon fingered an unspecified “organized group” behind the terrorist act, while President Vladimir Putin vowed to hunt down the criminals behind the mass murder, insisting that the attack demonstrated that his military intervention in Syria last year was correct, and that terrorists must be fought with vigor. Mr. Putin seemed embarrassed and angered by the loss of Flight 9268, which cast a pall over his otherwise impressive record of aggressively fighting terrorism against Russians.

Egyptian authorities, many of whom privately admitted a terrorist bomb likely did bring the jet down, publicly defended their government against charges of incompetence, not least because tourism is a big boost to the country’s economy. While Western intelligence agencies were troubled by the speed with which the Kremlin assembled its narrative, they did not dissent from the FSB’s basic conclusions. American and British spies agreed that the crash was caused by terrorism, and the latter possessed signals intelligence intercepts that placed blame on Islamist militants in the Sinai, who snuck a bomb into the jet’s baggage hold.

For their part, jihadists backed Kremlin claims. Affiliates of the Islamic State, the notorious ISIS, boasted of their responsibility for the attack, which seemed plausible since that group is at war with Russia, and their fighters are thick on the ground in the Sinai. Their claim was bolstered in mid-November when ISIS ran a photo of what purported to be the fatal bomb in their online magazine. The next day, the Russian defense minister publicly fingered ISIS fighters in the Sinai as the culprits behind the attack.

The ISIS-did-it narrative was thus firmly established in Moscow and was gaining credence in many quarters, over increasingly diffident objections from an embarrassed Cairo. Middle East events, however, intervened. On November 24, a Turkish Air Force fighter shot down a Russian Su-24 jet bomber on the border with Syria, killing its pilot and setting off a major regional crisis, complete with aggressive bluster on both sides, which has not yet ebbed away.

Russian security services have an impressive track record of spinning complex conspiratorial yarns to explain events; this may have something to do with the fact that their word for espionage tradecraft is konspiratsiya—’conspiracy.’

Suddenly ISIS, which Mr. Putin only months before compared to Nazism before the United Nations, demanding a World War Two-like coalition do defeat the Islamic State, was no longer Public Enemy Number One in Moscow, its place in Kremlin demonology having been abruptly taken by Turkish President Recep Erdoğan and his government.

Soon regime-friendly media in Russia was offering dark hints of a Turkish hand behind the destruction of Flight 9268. Recently these claims grew explicit, and in late January a Russian tabloid closely linked to Kremlin intelligence services asserted that the baggage handler who snuck the bomb onto the Airbus had last been seen in Turkey.

Now regime media in Moscow is claiming that Turkish terrorists, not ISIS, are behind the downing of Flight 9628. Citing anonymous FSB sources, this report asserts that the Grey Wolves, a militant group of Turkish ultra-nationalists, are the real culprits. The original Russian report posits a complex conspiracy involving collaboration between the Grey Wolves and ISIS in Egypt to take down Flight 9268. This FSB theory is long on speculation and very short on evidence.

Russian security services have an impressive track record of spinning complex conspiratorial yarns to explain events; this may have something to do with the fact that their word for espionage tradecraft is konspiratsiya—“conspiracy.” All the same, the Grey Wolves are a real terrorist group and they have a rising profile in Kremlin propaganda, dating to the deterioration of relations between Moscow and Ankara in the late autumn.

Moscow-linked sources have long depicted the Grey Wolves as the hidden hand of American intelligence, despite there being no credible evidence for this assertion.

Once things got nasty between Russia and Turkey, Kremlin outlets suddenly began to see Grey Wolves lurking menacingly all over the place: behind the murder of the downed Russian Air Force pilot in November, collaborating with Ukrainian “fascists,” perhaps even threatening the Kremlin’s hold on Crimea, which it occupied in March 2014. Evidence for any of this can charitably be termed thin.

But who exactly are the Grey Wolves? They have existed for nearly a half-century and possess a track record of fanaticism and violence. Motivated by hardline Turkish nationalism with more than a whiff of fascism, the Grey Wolves (Bozkurtlar in Turkish) have perpetrated numerous attacks on ethnic minorities over the years, including Kurds, Armenians and Alevis. They espouse a militant Pan-Turkic ideology, advocating the unification of most of Central Asia under Ankara’s rule. The Grey Wolves are notably anti-Russian and they dispatched small numbers of fighters to Chechnya to battle against Moscow in the wars that have torn apart that renegrade Russian province since the early 1990s. There are rumors that handfuls of Grey Wolves are fighting in Syria today against the Assad regime and their Russian allies.

Moscow-linked sources have long depicted the Grey Wolves as the hidden hand of American intelligence, despite there being no credible evidence for this assertion. That the group was a cut-out for the CIA was a standard Cold War trope that had advocates, including in Turkey, which is every bit as enamored with conspiracy as Russia. Turks of left-wing views found it easy to believe that the murderous Grey Wolves got support from right-wing Turkish military and intelligence officials with American backing; that Ankara really does covertly support certain terrorist groups made such assertions plausible. Kremlin propaganda has recently resurrected these explosive claims for political effect in the new round of sparring with Mr. Erdoğan.

The Grey Wolves’ alleged ties to the United States and NATO hinge on the supposed GLADIO conspiracy, which maintains that the CIA and the Pentagon clandestinely caused myriad political violence in Europe in the 1970s and 1980s. This theory has been given a veneer of academic credibility by dubious authors, but there’s no real evidence for it. The main “proof” of GLADIO’s nefarious activities is an alleged Pentagon manual that, in fact, has been known to be a KGB forgery for decades.

In 1981 the Kremlin was terrified of the Polish pope who, as the Solidarity movement in his native land threatened the whole Soviet empire, loomed as an archenemy in Moscow’s eyes.

In truth, if the Grey Wolves had ties to any Cold War intelligence services, they were those of the Soviet Bloc, not NATO. Links between the group and Bulgarian state security, the unsavory DS, were noticed by several Western intelligence agencies. The motivation was not ideology—the Grey Wolves hated Communists and Bulgarians equally—rather money: both engaged in drug-running as a cash cow. The DS earned a nasty reputation for such misdeeds as the assassination of troublesome émigrés, and its involvement in the international drug trade was known to spies in several countries.

Together the DS and the Grey Wolves were mixed up in one of the great unsolved mysteries of Cold War espionage, the attempted assassination of Pope John Paul II in May 1981. The gunman who nearly felled the pontiff in Rome, the Turkish nationalist Mehmet Ali Ağca, was a member of the Grey Wolves. On their behalf he murdered a prominent Turkish liberal journalist in early 1979 and, after a prison break, went on the lam, crisscrossing Europe, eventually winding up in St. Peter’s Square with a pistol, on a mission to murder the pope.

How Mr. Ağca funded his extended travels was never clear—somebody was supplying the wanted man with cash, sanctuary, and forged documents—and his extended stays in Bulgaria, at hotels known to be run by the DS, have never been adequately explained. Italian intelligence learned that, while in Rome before the assassination attempt, Mr. Ağca was in the company of the top DS officers living under cover in Rome. Moreover, some of those DS officers were actually in St. Peter’s Square when the would-be assassin shot Pope John Paul II.

Thirty-five years later, who stood behind Mr. Ağca remains murky. Released from prison in 2010, he has told so many different versions of events—including stating at times that the DS employed him to kill the pontiff—that Mr. Ağca cannot be considered a reliable witness. That the DS was the most subservient of all the East Bloc security services to Moscow, functioning as a branch office of the KGB, is not disputed. Neither is the reality that, in 1981, the Kremlin was terrified of the Polish pope who, as the Solidarity movement in his native land threatened the whole Soviet empire, loomed as an archenemy in Moscow’s eyes.

Did the Grey Wolves nearly kill Pope John Paul II, who was canonized a saint in 2014? Was this a joint operation with the Bulgarian secret services, their partners in drug crime, on Moscow’s behalf? The full truth may never be known and the debate remains long on speculation and short on hard evidence.

Regardless, it seems more than a little ironic that the Kremlin has recently brought back the Grey Wolves as their preferred international bogeyman. It’s difficult to discern why that group would partner with ISIS, since the Grey Wolves hate Islamists and utterly reject their aims, which are deeply at odds with their Turkish nationalism. That ISIS stands behind this atrocity, Moscow’s original line, seems far more plausible.

Moscow’s revised propaganda is consistent with presenting Ankara as the “real” force behind ISIS, which is a now-standard trope in Russian media. “Low-grade Kremlin bullshit” was how a senior American intelligence official with extensive experience in the region described the current Moscow line on the Grey Wolves: “trying to pin the airline disaster on Ankara this way is sure to kick the hornet’s nest in Turkey.”

That the Grey Wolves, not the Islamic State, murdered 224 innocent people is a far-reaching claim that requires genuine evidence to be taken seriously. To date, none has been forthcoming. If Moscow has such evidence, it needs to present it to the world, before the rising tensions it’s creating with Turkey threaten to engulf an already dangerously unstable region.