He doesn't necessarily need to be "clever and Macchiavellian" to be privy to that kind of knowledge about her. Politicians have connections, that's just a plain fact. And those connections aren't always necessarily confined by party lines. You know, "six* degrees of separation" and all that.
Reid met her a few times when she was shepherding through nominations. She was probably very polite to Reid during the filibusters.
Now that's crazy. Politicians, especially those who've gotten to where he's gotten, know better than to let themselves get schmoozled by close associates of their political enemies. What I'm trying to squeeze out of you is that Reid recommended to the President someone whom the President knew very closely, but whom Reid knew not at all. How could he possibly have become Senate Minority Leader by being that clueless?
(* usually much fewer than that in the world of Washington politics)
He had to put down a list of names. That's it. So he picked her because he thought she'd never be picked. Again, what does Reid know that Bush doesn't?