Tom - PC = Politically Correct. I.E. going to ridiculous lengths to not offend anyone. Unless they're rich white males. Then you can beat them over the head with a brick. Check out "PCU" the next time it's on FX - it's funny, but some parts are so true to life it's kinda not funny.
Leslie - recognition by the college or university gives you several advantages. You can use on-campus buildings, you (or more likely, the IFC/Panhel) receives $$ from the student activities fund, and you can advertise and hold your events on campus. Also (but not so much anymore) the college might step in to CYA if you get in trouble.
I don't think recognition will matter at Dartmouth, because the Greeks are around 50% of students, and most students who aren't Greek aren't anti cause all the parties are open. Plus they've got enough $$$ and alumni support to keep it going even if they have to move all their houses to a neighboring town. There's an article on DKE's website in the news section (they have a lot of good stuff on things like this, by the way) where a Middlebury alum said that even though the administration "banned" fraternities, they are still going strong.
Like KSig said, all I have seen on this issue is that they got rid of bars and kegerators. Just a bunch of BS PR.