Rumsfeld and Cheney volunteered to help Nixon when he was sinking, but Nixon did not trust Rumsfeld (he didn’t know Cheney). Needless to say, it is pure speculation as to what Rummy and Dick “learned” from Watergate. I gave my views on the Bush/Cheney/Rumsfeld presidency in Worse Than Watergate, explaining how they imposed secrecy way beyond Nixon. This was how they got away with blatant violations of law that make Watergate look like little league. I am not sure that Richard Nixon in one of his darkest moods would have authorized torture!
Nixon served in the South Pacific during WWII, and was familiar with the horrors of Japanese torture, so I cannot believe he would have lowered the USA to tolerate such horrific behavior. With foreign policy, Nixon seemed to understand what today we call “blow-back” and that by our engaging in torture he would expose Americans soldiers (if not all Americans) to torture, just as we are seeing with Americans being captured by ISIL. Bush/Cheney have subjected any and every American kidnapped or captured to torture by the likes of ISIL. It is a decision that is going to haunt us and the world for untold decades.