that is a straight up LIE because I was talking to a partner from Williams & Connolly (Stanford alum) a couple of months ago and she said that even when she was at Stanford (10 years ago) everyone wanted WLRK and she said not much has changed since.
I'm the anon above.
No, it's not a lie, and sorry to burst your bubble but that's definitely not the case at Stanford anymore. I'm a 2L at Stanford, on law review, and probably somewhere around top 10% (although who really knows). I didn't bid for WLRK and I certainly wasn't alone among top students or those on law review. I would be pretty shocked if the majority of SLR 2Ls even so much as bid on WLRK. Even among those SLS students who are looking to go to NYC (as the poster above described, this is a minority of the class), WLRK isn't uniformly those students' top choice. First, people here really do care a lot about quality of life--it's a significant reason why a lot of us came to Stanford specifically. And, second, WLRK is really even only arguably the "best" for transactional work, and I'd guess that a minority of those looking to go to firms here want to do transactional. But most of all, my sense is that a majority of the class didn't bid on more than a handful of NYC firms (and if you're going to go for 1, it's typically not going to be WLRK).
My sense of the "desired" firms here at Stanford is that boutiques and specialty firms are popular--Jenner DC, Irell, Keker, Munger, etc (not tops in Vault, but excellent at what they do). Mofo, which has a big campus presence, definitely has more SAs than you'd expect, although I don't think it's one of the most competitive firms.
I'd be surprised if this is different at Yale, but hey, maybe it is--most students at Stanford got into Harvard or Yale or both (just as most students at Yale got into Stanford and Harvard, and many students at Harvard got into Stanford and Yale), and therefore it is a pretty self-selected group of students who end up here. Sure, people, for the most part, keep jumping through the "prestige" hoops even after getting into Stanford, but people really don't care much about Vault rankings or whatnot here--the gold stars people strive for at Stanford are things like clerkships, the Supreme Court Clinic (although trust me, the Clinic's definitely not for everybody), and to a lesser extent Law Review.