Trump gave no source for his claim but he made it half an hour after Fox News' Fox & Friends account had passed along a Fox News segment in which the same assertion had been made. Fill in the standard appropriate disbelief/bemusement/horror at the President of the United States, with all the resources of the U.S. government at his command, getting his "information" instead from political fantasists like Fox News. Right-wing figures have made similar claims about former Guantanamo prisoners for years. The fact-checkers went to work on this one today but while they refuted part of Trump's claim, they uncritically employed extremely dubious information provided by the government, information past analysis suggests grossly inflates actual recidivism by Guantanamo detainees.
Rebecca Shahab at CBS News:
"The number  appears to stem from a report released last September from the Office of the Director of National Intelligence, but the report clearly indicates that 122 of the 693 detainees, or about 18 percent, released under both George W. Bush and Obama administrations reengaged.Shahab's use of Trump's word "released" is potentially problematic, as many of those who are "released" are, in fact, transferred to the control of foreign governments, not, as that word implies, simply set free.
"A bulk of those detainees that returned to the battlefield, however, were released under the Bush administration, before the U.S. set up an interagency screening and hearing process for each prisoner. The report says that of the 532 detainees released from the detention facility under Bush, 113 returned to the battlefield, or about 21 percent.
"Under Obama, 161 detainees were transferred from Guantanamo Bay and only 9 have been confirmed to have reengaged and returned to the battlefield. That’s just under 6 percent of the total transferred since 2009.
"Of the combined total 122 that returned to the battlefield under both Bush and Obama, the report says that 30 are dead, 25 are in custody and 67 are not in custody."
FactCheck.Org's Robert Farley used the same report (but also the same problematic wording), concluding that Trump's claim was "simply false"; the overwhelming majority of those 122 were released by the Bush administration.
Politifact's Lauren Carroll uses the same figures: over 92% of those "the government believes have returned to some sort of terrorist activity" were transferred under Bush. On the terminology, Carroll, to her credit, is more careful and quotes DePaul University counterrorism professor Thomas Mockaitis pointing out that "many of those released are handed over to foreign states who assume responsibility for them." Carroll also references a 2014 report by the New America Foundation which investigated confirmed or suspected "militant activity" by former detainees and could only confirm 1/3 of the cases claimed by the government at the time.
Rather than spurring further investigation, that last bit of info is just left to lie there unexamined while Carroll rates Trump's claim "mostly false."
The government's claims with regard to recidivism by former Guantanamo detainees, which have been made in a periodically-issued report for many years, have long been called into serious question. The Center for Policy and Research at the Seton Hall University School of Law, which has released over 15 reports on issues related to the detainees, has tackled the recidivism claims repeatedly. Among other things, the government can't document most of its claims of recidivism. It consistently makes sweeping assertions regarding this matter while refusing to name most of the alleged recidivists or provide any real information on their alleged recidivism. The material cited by the fact-checkers are just asserted numbers. Empty claims, and not consistent ones either--the number of asserted recidivists goes up and down over the years. With regard to the much smaller group who have actually been named, the government's assertions are rife with problems. Contradictions abound. While "recidivist" clearly suggests someone who was guilty of some past offense returning to commit further offenses, most of the Guantanamo detainees--55%--were "not determined to have committed any hostile acts against the United States or its coalition allies," which shouldn't be surprising given the fact that only 5% of them were captured by U.S. forces in the first place; the rest were, instead, turned over by third parties in exchange for U.S.-provided bounties on those who were supposed to be al Qaida or Taliban fighters. In so impoverished a country as Afghanistan, a get-rich-quick scheme. Some named were, in fact, never detained at Guantanamo at all. For years, the government conflated numbers on those whom it asserted had committed actual recidivist offenses and those merely suspected of doing so, admitting that some of the claims were based on unconfirmed, single-source reporting. Makes the number look bigger, see? For a long time, the government even identified as recidivists those who had merely written articles critical of their own detention or had publicly spoken out against same, a policy now discontinued but one that, like most of the rest of this, speaks to the bad faith of the government's claims. Remarkably, "the government admitted that its primary source of information was reporting by the press, not government intelligence," which makes the refusal to provide names to go with most of the claims even more suspect, as the names of everyone who had been detained at Guantanamo have been public information for years.
To put the matter bluntly, the government's claims in this matter are bullshit. They've been bullshit for over a decade.
So while the fact-checkers have refuted part of Trump's claim, the dubious nature of the information on which those refutations rest--and which the fact-checkers mostly ignore--suggest the scale of his lie may be much larger than even those refutations suggest.
 Farley further notes that the Trump regime made a similar claim only a few weeks ago and was corrected by FactCheck then as well:
"On Feb. 22, we wrote, Sebastian Gorka, a deputy assistant to the president, wrongly suggested that a released Guantanamo Bay detainee responsible for a recent suicide bombing in Iraq was released by Obama. He was transferred from Gitmo in 2004 under President Bush. Gorka also wrongly claimed that among detainees released by Obama, 'almost half the time, they returned to the battlefield.' According to the Office of the Director of National Intelligence, about 12.4 percent of those transferred from Gitmo under Obama are either confirmed or suspected of reengaging. As those reports have been released over the years, they've been almost entirely ignored by the corporate press. Having the fact-checkers now ignore them is, unfortunately, nothing new.
"As we noted then, most of the former Gitmo detainees who are now suspected or confirmed to have reengaged were transferred or released under President Bush. Bush transferred a higher number of detainees--532 compared to 161 under Obama--and they have been reengaging (or are suspected of reengaging) at a higher rate — 35 percent compared to 12.4 percent under Obama. That may change over time, but those were the percentages as of last July."
 The Center's March 2012 report even makes a chart of these shifting claims over three years:
 Even if one takes the government's worst-case assertions at face value, most detainees who were transferred have never become "recidivists." The actual documented cases of subsequent offenses are a much smaller number. The focus on alleged recidivists, rather than the bulk of detainees who aren't known to have ever committed any offense, is political, aimed at justifying the continuing existence of the GTMO detention facility when the known facts actually show it's been used to lock up people for years on end who have never been any threat to anyone.