Hi friends,
I'm a current Ph.D. student at UC (HB/NWS) and can vouch for at least the Div School and NELC being largely free of the sort of detrimental competition you mention above. There's a lot of camaraderie among Masters and Ph.D. students -- many of the students who had been there for a while when I showed up were especially friendly and helpful. The work's tough, of course, but people definitely aren't out to get one another and the seminar atmosphere is generally pretty relaxed.
Hope this helps. Glad to hear, matthew2725, that you had a good visit!