Washington (CNN) President Donald Trump is facing intense criticism over a July phone call during which, according to a person familiar with the matter, he pressed Ukrainian President Volodymyr Zelensky to investigate the son of former Vice President Joe Biden, a leading candidate to face him in the 2020 presidential election.

Under fire, Trump has revived one of his favorite defensive tactics: trying to turn the spotlight onto his opponent.

Trump has made a series of allegations about Joe Biden and his son Hunter Biden over the last week. The essence of Trump's argument is that Joe Biden was improperly trying to help Hunter, who served on the board of a Ukrainian natural gas company, when Joe Biden pressured the Ukrainian government to fire the country's prosecutor general.

But there are significant holes in Trump's story. Some of his allegations have been false. Others have been missing important context.

Trump's missing context: What happened with the Ukrainian prosecutor

In castigating Biden's effort to get the prosecutor general fired, Trump has declined to mention an important fact: a whole lot of other people were also trying to get him fired at the time.

The Obama administration, American allies, the International Monetary Fund and Ukrainian anti-corruption activists , among others, had all made clear that they were displeased with the performance of Viktor Shokin, who became prosecutor general in 2015.

The International Monetary Fund warned Ukraine in February 2016 that it risked losing financial support if it did not clean up its act. The Financial Times explained in its article on the warning that then-President Petro Poroshenko was facing pressure to replace Shokin, whom the newspaper described as a "long-time loyalist" of the president; the article continued, "Mr. Shokin has been criticized for failing to bring to justice any of the snipers who killed dozens of protesters in central Kiev in the final days of the revolution, and for dragging his feet over investigating senior officials and businesspeople."

In a September 2015 speech, the US ambassador to Ukraine, Geoffrey Pyatt, used blunt language in criticizing Shokin, blasting "corrupt actors within the Prosecutor General's Office" who were "making things worse by openly and aggressively undermining reform." Then, during a visit to Ukraine, Biden, who had long handled Ukraine issues for the Obama administration , applied public and private pressure on the government.

In a speech to Ukraine's legislature, Biden said , "The Office of the General Prosecutor desperately needs reform."

The most detailed account of Biden's private words comes from Biden himself. At a Council on Foreign Relations event in 2018, he recounted that he had threatened to withhold a "billion-dollar loan guarantee" unless Poroshenko followed through on what Biden said was a "commitment" to "take action against the state prosecutor."

"I looked at them and said: 'I'm leaving in six hours. If the prosecutor is not fired, you're not getting the money.' Well, son of a bitch. He got fired. And they put in place someone who was solid at the time," Biden said.

The timeline here is fuzzy: Shokin was not actually terminated while Biden was in the country, as Biden's story made it sound. Ukraine's legislature voted to fire Shokin in March 2016; Biden's last visit to Ukraine before the firing was in December 2015. Biden did have a phone call with Poroshenko the week before the dismissal.

Biden spokesman Andrew Bates told CNN that Shokin's removal was a "focus" for Biden "during numerous trips and phone conversations," since the prosecutor was such a major impediment to anti-corruption efforts.

What Trump has been getting wrong

Trump is free to criticize Hunter Biden for taking a position with a Ukrainian company at the same time as his father was directly involved in Ukrainian issues. And Trump is free to criticize Joe Biden for declining to recuse himself from a matter that could conceivably have affected his son's interests.

But Trump has been inaccurate about some of the key facts of the situation.

Claim 1: Trump says Biden called for the firing of a prosecutor "investigating his son"

Trump has repeatedly claimed Shokin was investigating Hunter Biden. For example, Trump alleged Saturday that the media wants to avoid talking about the "Joe Biden demand that the Ukrainian Government fire a prosecutor who was investigating his son..."

But there is no public evidence that Hunter Biden was ever himself under investigation.

The investigation, as far as we know, was into the business activities of Mykola Zlochevsky, who owned a natural gas company, Burisma Holdings, for which Hunter Biden had sat on the board of directors since 2014 . The United Kingdom had begun investigating Zlochevsky before Hunter Biden joined the board.

"Hunter Biden did not violate any Ukrainian laws -- at least as of now, we do not see any wrongdoing," Shokin's successor as prosecutor general, Yuriy Lutsenko, told Bloomberg . Of a 2013 business transaction that was part of the investigation, Lutsenko said, "(Hunter) Biden was definitely not involved. We do not have any grounds to think that there was any wrongdoing starting from 2014."

It is not clear how hard Shokin was investigating even Zlochevsky or Burisma at the time Joe Biden pushed for Shokin's firing. Kasko, the prosecutor who resigned from Shokin's office, told Bloomberg that the case was dormant at the time of Joe Biden's intervention: "There was no pressure from anyone from the US to close cases against Zlochevsky. It was shelved by Ukrainian prosecutors in 2014 and through 2015."

Shokin told The Hill for an April 2019 article that he had made "specific plans" before his firing that "included interrogations and other crime-investigation procedures into all members of the executive board, including Hunter Biden."

But his assertion that the investigation was active has been challenged.

"Shokin was not investigating. He didn't want to investigate Burisma," Daria Kaleniuk, executive director of Ukraine's Anti-Corruption Action Center, told the Washington Post for a July article. "And Shokin was fired not because he wanted to do that investigation, but quite to the contrary, because he failed that investigation."

Claim 2: Trump says Biden told Ukraine to take Shokin off the case

"Somebody ought to look into Joe Biden's statement, because it was disgraceful, where he talked about billions of dollars that he's not giving to a certain country unless a certain prosecutor is taken off the case," Trump said last week.

There is no evidence Biden ever called for Shokin to be "taken off the case." In fact, there is no evidence that Biden mentioned the case at all when discussing Shokin with Ukrainian officials. Rather, Biden generally pressured the Ukrainians to fire Shokin, according to reporting from multiple news outlets and Biden's own account of what happened.

Trump's allies might argue that calling for the prosecutor's firing was even worse than calling for him to be taken off a particular case. But there is a key difference given the context.

Had Biden called for Shokin to be taken off a particular matter in which his son had a stake, this would seem to suggest that his motivation was helping his son. But Biden calling for Shokin's firing, without mentioning that particular case, was consistent with the international concern about Shokin's performance.

Claim 3: Trump says Joe Biden previously said he spoke to Hunter Biden about Hunter's business dealings

Biden said Saturday, "I have never spoken to my son about his overseas business dealings." Trump responded Sunday, "He also said, long before, that he did speak to his son. So he lied, again."

Biden has not previously said that he did speak to his son about his overseas business dealings. Rather, it was Hunter Biden who said that there was a conversation on the subject, according to a New Yorker article in July.

That article said this: "As Hunter recalled, his father discussed Burisma with him just once: 'Dad said, "I hope you know what you are doing," and I said, "I do.'"

Once is more than never, so Trump can fairly point out the contradiction -- though the New Yorker article did not offer evidence that the father-son exchange was detailed. Regardless, the elder Biden was not contradicting himself; he was contradicting his son.

Claim 4: The amount of money at issue

Trump has repeatedly alleged that Biden threatened to deny Ukraine "billions of dollars." According to Biden, it was a $1 billion loan guarantee. (Less than three months after Shokin was fired, Obama agreed to approve a $1 billion guarantee.)

We don't have independent confirmation of what was discussed, so it's possible that Biden had also raised the subject of additional funds.

One general caveat: it is possible that we'll generally learn more about Hunter Biden's work in Ukraine and about the firing of Shokin. But what we know right now shows significant factual problems with Trump's theories.