Don't mean to point out the obvious, but TFA states that Obama's now the defendant, not Bush, because Obama's now the president. Requesting a stay only means that he's buying some time. I'd do the same if I found myself in a new job being sued for what my predecessor did.
On the other hand, he can disagree with spying on US citizens but still support immunity for the telecoms. A private company (or individual) should not be punished for cooperating with the government when the government was doing something illegal. Sure, its a Nuremberg defense, but the difference here is that we're talking about a legally ambiguous request, not a heinous immoral act like genocide or DRM.
Ontogeny recapitulates phylogeny.