The rhetorical war over the U.S. national security space launch program reached a fever pitch in May amid the confluence of Space Exploration Technologies Corp.’s lawsuit challenging the U.S. Air Force’s sole-source rocket contract with United Launch Alliance and Russian threats to restrict the use of Russian-built engines on a ULA workhorse vehicle.

Not surprisingly, SpaceX Chief Executive Elon Musk, who made his fortune in the tech business, has taken the battle to Twitter, which allows him to instantly reach a global mass audience with short bursts of commentary. Unfortunately, Mr. Musk has crossed a line in publicly accusing, via Twitter, a former Air Force rocket buyer of improperly leveraging that position to land a cushy job with Aerojet Rocketdyne, a key ULA supplier.

The official in question is Roger S. Correll, who until recently was the Air Force’s program executive officer for space launch. According to the National Legal and Policy Center (NLPC), an organization dedicated to promoting ethics in public life, Mr. Correll, a civilian, negotiated the $11 billion block buy of 36 launch vehicle cores from ULA on behalf of the Air Force, then turned around and went to work for Aerojet Rocketdyne as vice president for government acquisition and policy.

In a May 18 post on its website, the NLPC cited Mr. Correll’s hiring as yet another example of the so-called revolving door that sees influential U.S. government officials going to work for companies with which their agencies routinely do business. The article noted that this practice has been associated with scandal in the past — it specifically cited one infamous case — but stopped short of actually accusing Mr. Correll or Aerojet Rocketdyne of any wrongdoing.

Mr. Musk exercised no such restraint. In a tweet posted May 22, he did his best to slap a guilty verdict on ULA, Aerojet Rocketdyne and Mr. Correll: “V likely AF official Correll was told by ULA/Rocketdyne that a rich VP job was his if he gave them a sole source contract.”

V likely AF official Correll was told by ULA/Rocketdyne that a rich VP job was his if he gave them a sole source contract — Elon Musk (@elonmusk) May 23, 2014

In a subsequent tweet, Mr. Musk offered his evidence: “Reason I believe this is likely is that Correll first tried to work at SpaceX, but we turned him down. Our competitor, it seems, did not.”

Those tweets were way out of line. In the first place, whatever role Mr. Correll played in negotiating the ULA contract, the decision to do the block buy in the first place was not his — it came from the very top of the Pentagon acquisition hierarchy. Frank Kendall, undersecretary of defense for acquisition, technology and logistics, ordered the block buy in 2012 as part of a two-pronged strategy for bringing down the Defense Department’s launch costs, the other prong being the introduction of competition.

Secondly, even if Mr. Correll was turned down for a job at SpaceX, so what? If anything, that only suggests there was no quid pro quo involving Aerojet Rocketdyne, since Mr. Correll otherwise would have little reason to seek employment with SpaceX.

Besides, the pool of companies that would be inclined to pay top dollar to someone with Mr. Correll’s expertise is a small one, which obviously includes SpaceX and Aerojet Rocketdyne. Mr. Musk himself is not above playing the revolving-door game: It’s no secret that SpaceX has put former government officials involved in the space launch enterprise on its payroll.

Mr. Musk is of course entitled to voice his opinion, and certainly he has a huge stake in this matter. But his public indictment, on the basis of appearance alone, reeks of sour grapes. It was a cheap shot at best; at worst, it was a cynical ploy designed to sell the narrative that SpaceX is not getting a fair shake from the Air Force.

Either way, Mr. Musk has unfairly, perhaps irreparably, impugned reputations. Bear in mind that Mr. Musk has nearly 700,000 Twitter followers — an audience approaching the subscribership of two widely read magazines, The Economist and Wired — and his tweets were picked up as news stories by leading outlets including the Associated Press and The Washington Post.

In the wake of the NLPC article, SpaceX amended its legal challenge to the block-buy contract to note Mr. Correll’s hiring. Separately, Mr. Musk has called for, via Twitter, the Air Force inspector general to investigate the matter.

That’s fair play. Revolving-door hires can indeed turn out to be as shady as they initially appear, the most obvious example being that of Darleen Druyun, the former top Air Force acquisition official who was convicted of corruption after taking a job with Boeing, to which she had just awarded a multibillion-dollar contract for refueling tanker aircraft.

If the appropriate U.S. authorities smell something fishy in this case and opt to launch an investigation, so be it. But Mr. Musk’s warrantless accusations are of no help in this regard. They can only complicate that decision while soiling the reputations of people who, based on currently available evidence at least, have done nothing wrong.