Apparently they caused quite a ruckus at the post-fight press conference.
According to this article from SI.com (http://sportsillustrated.cnn.com/2008/mma/09/18/nick.diaz/index.html):
...Nate had barely taken his seat in front of reporters at the post-fight press conference when his older brother Nick launched into a tirade that disrupted the interview and left the UFC staff with the unenviable task of keeping the Diaz clan from causing a scene. Good luck with that one.
Nate abandoned the press conference as his brother shouted profanities at no one in particular, and together they took their rant into the hallway.
I seriously wonder if Nick isn't getting jealous of Nates success and trying to throw a monkey wrench in there. Seems a bit like it to me. No idea why he was flipping out, but we always see Nate saying nice things about Nick, and we always see Nick acting like... well, Nick. Maybe it's time for Nate to grow up and make his own path instead of tying his chain to the sinking, and self-destructive, Nick.