As weird is as it sounds, this is exactly what happened. Some countries have laws against torture and there is the Geneva Conventions. One of these countries is the US. In the wake of 9/11, the US government sought to "loosen up" the laws so harsher techniques can be used when interrogating suspected terrorists.
But that was not enough for some people, particularly those in the Pentagon and the CIA so they came up with an ingenious idea – why not outsource it to the some of our allies? Some of the closest allies of the US in the Middle East are lets say "Pro-Torture" who embrace torture whole-heartedly and would be happy to lend their services to the US (after all, what is torture of couple of terrorists among friends). So, the CIA would ship suspected terrorists to various countries in the Middle East - mainly Egypt, Jordan and Saudi – to be tortured by the experts.
How about that for outsourcing?