On the topic of schools and supporting torture in client regimes, remember that someone had to both negotiate with the UAE in order to convince them that it would be in their best interest to do as the US says on the topic of torturing foreigners, as well as teach UAE's security forces how to torture in the US-approved way. That way, when someone the US wants information from comes along, they can be tortured by the UAE so that US can keep its PR.
Think about that for a minute. The US is teaching third parties how to torture effectively on its behalf because it wants the torturing done to the proper standard and because it is afraid of the backlash that will occur when torture is exposed. From this thought, we can say that the US has extensive internal standards regarding what methods of torture are acceptable and useful for clients to know, which are likely influenced by how bad and how directly attributable these torture techniques will look when exposed.
A speculation: the US still tortures people directly in addition to third party torture. They already have the secrecy, infrastructure, training, standards, incentive, and targets in hand.