The drum that schools like ASU have been banging is not that they share revenue, but that the schools' athletic association opens up the doors for additional academic association. It's not codified in the conference bylaws (like the B1G's Academic Alliance), but the school presidents would be hard pressed to say they only discuss athletics outside of the conference rooms when they meet semi-annually. The schools that align together in the athletic conference (Pac-12) also align together and help each other as institutions, including research projects.
You are correct that research funding isn't pooled and split across the members of the athletic conference. The argument made by the people in charge at Utah and ASU has been that by associating with schools like Stanford they increase their potential funding from research.
Personally, I don't know anything about this. If you do, then I'm happy to defer.