The automatic assumption about the CIA's destruction of the interrogation tapes of Abu Zubaydah is that the tapes exposed methods everyone would agree amounted to torture, and they were destroyed to prevent that proof being exposed. It's quite likely that what was being covered up was the results of that torture.
Gerald Posner has a piece at HuffPo drawing from his 2003 book that is worth a read:
Instead, when confronted by his "Saudi" interrogators, Zubaydah showed no fear. Instead, according to the two U.S. intelligence sources that provided me the details, he seemed relieved. The man who had been reluctant to even confirm his identity to his U.S. captors, suddenly talked animatedly. He was happy to see them, he said, because he feared the Americans would kill him. He then asked his interrogators to call a senior member of the Saudi royal family. And Zubaydah provided a private home number and a cell phone number from memory. "He will tell you what to do," Zubaydah assured them
He named two other Saudi princes, and also the chief of Pakistan's air force, as his major contacts. Moreover, he stunned his interrogators, by charging that two of the men, the King's nephew, and the Pakistani Air Force chief, knew a major terror operation was planned for America on 9/11.
It would be nice to further investigate the men named by Zubaydah, but that is not possible. All four identified by Zubaydah are now dead. As for the three Saudi princes, the King's 43-year-old nephew, Prince Ahmed, died of either a heart attack or blood clot, depending on which report you believe, after having liposuction in Riyadh's top hospital; the second, 41-year-old Prince Sultan bin Faisal bin Turki al-Saud, died the following day in a one car accident, on his way to the funeral of Prince Ahmed; and one week later, the third Saudi prince named by Zubaydah, 25-year-old Prince Fahd bin Turki bin Saud al-Kabir, died, according to the Saudi Royal Court, "of thirst." The head of Pakistan's Air Force, Mushaf Ali Mir, was the last to go. He died, together with his wife and fifteen of his top aides, when his plane blew up -- suspected as sabotage -- in February 2003. Pakistan's investigation of the explosion -- if one was even done -- has never been made public.
It wasn't the fact that he was tortured that needed covering up, it was what he said.