I became a full professor at the University of Wisconsin-Madison in 2001. Among the responsibilities of full professors are (1) to evaluate whether professor at schools other than ours merit promotion and (2) to chair and serve on promotion committees at our own schools.
So far as I can tell, senior faculty take these responsibilities very seriously. The strange part is that we take promotions of people at other schools very seriously, even though we compete with those very schools. I suppose one could make an argument that we at USC should try to blow up the cases of those who we deem to be good at other schools in California, while also waxing enthusiastic about weaker faculty at these schools. It is as if Honda were telling Toyota who to promote, and vice versa.
In the end, though, faculty at one school tend to recommend that faculty they deem meritorious at another receive promotion. While the process is certainly less than perfect, the good faith that most faculty show in these affairs helps explain why the US still has the best research universities in the world.