Let the record show that these claims are misleading in the extreme.

The most prominent test case where a single terrorist suspect was interrogated using both the F.B.I.’s traditional approach and the C.I.A.’s enhanced techniques was Abu Zubaydah, the first high-value Qaeda operative captured after Sept. 11. Held at a C.I.A. secret “black site” prison, Mr. Zubaydah, who was badly wounded during his capture in Pakistan, was initially interrogated by a two-man F.B.I. team consisting of Special Agents Steve Gaudin and Ali Soufan. They went well beyond “tea and sympathy,” to the point of reading the suspect passages from the Quran as he hovered close to death. By building a rapport with the suspect and painstakingly breaking down his cover story, the agents learned for the first time from Mr. Zubaydah that the mastermind of the 9/11 attacks was Khalid Shaikh Mohammed. They also extracted the potentially critical intelligence that an American Qaeda operative, Jose Padilla, was plotting to explode a radiological “dirty bomb” inside the United States.

Later the C.I.A. took over the interrogation, and for the first time a prisoner was subjected to the regime of “learned helplessness.” The methods included sleep deprivation, hard slaps, stress positions, prolonged confinement in coffin-like containers and more than 80 rounds of mock drowning. The torment so profoundly disturbed C.I.A. personnel that some were “to the point of tears and choking up,” as a team member wrote in an email published in a 2014 report by the Senate Select Committee on Intelligence. At the end of it, Mr. Zubaydah was indeed a broken man, but he had surrendered no more actionable intelligence.

In an Orwellian twist, Mr. Mitchell and Mr. Jessen concluded that their experiment had succeeded because it proved that Mr. Zubaydah could not possibly have any additional intelligence to surrender. In a later brief to the president, senior C.I.A. officials summarized some of the “key intelligence” gleaned from Mr. Zubaydah as information identifying Khalid Shaikh Mohammed as the mastermind of 9/11, and the terrorist suspect Jose Padilla, both of whom were later captured. No mention was made that the critical intelligence was gleaned by F.B.I. agents without using torture.

By that point the F.B.I. had wisely distanced itself from the C.I.A.’s interrogation program. The bureau sent profilers from its Behavioral Analysis Unit to interview failed suicide bombers in Afghanistan to better understand their motivations and psychology. Armed with those insights, and using its traditional approach, the bureau gleaned important intelligence from the would-be New York subway bomber Najibullah Zazi; the would-be Times Square bomber Faisal Shahzad; and the “underwear bomber” Umar Farouk Abdulmutallab, who wanted to bring down a Northwest Airlines flight over Detroit.

In calling for a return to waterboarding, Mr. Trump was playing to the crowd. A Reuters/Ipsos poll conducted last year found that nearly two-thirds of Americans believe that torture of terrorism suspects can be justified. But a number of Mr. Trump’s cabinet nominees have recently made clear they disagree, including his pick for secretary of defense, Gen. James Mattis; for C.I.A. director, Representative Mike Pompeo; for attorney general, Senator Jeff Sessions; and for secretary of state, Rex Tillerson.