The extreme competition seems to be overtaking all of the elites. MIT is the #1 university brand in the world, but it spent most of its integrity and soul to get there.
There's a fine line you need to walk to become a faculty member at elite schools.
You need to lie a little on grant applications to align when you want to do to what will be funded. You need to lie a little bit in publications so they have impact. You need to fight for credit, sometimes on work you didn't do. As these become normalized, winners do these more and more; otherwise, you won't get that faculty job.
The culture slowly trickles down. I think most grad students at MIT are still honest, but not the most successful ones (most of the ones who find faculty jobs are at least a little bit crooked). Second-tier school faculty slots are filled with graduates of first-tier schools.
MIT has a traditional hacking culture which emphasizes breaking rules. This worked well when this involved climbing on rooftops, but it works less well when the endowment is O($100M) per faculty member, and there's money to embezzle through complex corporate schemes and financial games.
Contentions don't exist too much between faculty and admin right now, but they definitely do between students and Institute. MIT grad students are working to unionize, and the Institute, to union-bust.