The APA is a meaningless organization. They have zero authority over licensing. They also aren't the only professional psychological organization. APA membership carries with it no particular value; clients don't care about APA membership, they care about licensing.
The value of an APA membership is primarily that it makes access to published research affordable. If someone wasn't interested in accessing journal content, or required to present at conferences requiring APA membership to further their careers, I can't imagine why they'd pay to join.
I briefly looked before making my comment in another thread, I don't think the APA has any say over licensing (it's done by the states).
As to reasons why they might anyway, they believe the interrogation is worthwhile, a sense of duty to country, money, etc (I'm not saying those are reasons I agree with, I'm saying they are reasons someone might use to justify participation to themselves).
Absolutely. They have repeatedly turned to nationals from other countries to inflict cruelty upon detainees; why do you suppose they'd exclude psychologists in particular?
They'll turn to other countries for turnkey services, i.e. we hand you this person and maybe some cash and you'll tell us what you learned, if only because it's politically unfeasible to do it ourselves. Having been around government service most of my life, I can tell you that we're pretty lazy in that regard, so I can see why we'd practice rendition. Intelligence is already a really mercenary field, so our normal distrust of foreigners might well be disregarded in special circumstances.
I don't think that portions of services we are already providing, we'd contract, not just to some other American company, but to extra-national contractors, for tasks more complicated than manning customer-service-type posts, like mess halls. It's not the American way. When the service gets complicated, such as for maintenance of complicated military hardware, the government prefers to hire American contractors that use American workers, even specifying nationality in the contracts. It's a cultural thing.
Americans just don't trust foreign nationals. I could never see them trusting foreign psychologists, it flies in the face of everything I could ever consider to be "American".
I think they can probably find them.