I don't think it's because they are getting paid off. I also don't think that it is because most of them harbor secret, anti-American sentiments (though some may). Rather, I believe it is a combination of a) a desire to work on sexy, high profile issues that are more exciting than the cases on which they bill most of their hours, anbd b) a sometimes-misguided sense of noblesse oblige combined with a desire to "make a difference."
I'll add a third: nothing might be more exciting for a lawyer than getting factually-innocent defendants free from jail, and given the evidence, these lawyers may actually believe and have good reason to believe their clients are completely innocent. Adler missed that motive.
Mitigating this oversight, though, is Adler's belief that Gitmo detainees deserve a fair hearing, a belief not shared by the other authors at The Corner.