About the Big East thing...
1st invite:
When the Big East was 1st getting created in the 1970's they wanted Rutgers to be in it. Rutgers helped create and founded the conference that is today known as the A10. So they didn't want to leave them so quickly after creating it just to join a new conference, so they turn them down. The Big East ended up inviting SHU instead to rep NJ.
2nd Invite: Penn State, Rutgers, Pitt, Temple, UWV and a few others schools were talks about creating an all sports conference. Penn State wanted Pitt to join to act as the two big anchors. The Big East were scared that their two football playing members Cuse and Boston College would leave to join this new conference if it was ever created. So they tried to break it up before it got started. They offered membership to Rutgers to join, but Rutgers turned them down again, since they were trying to get this new conference going. The Big East then offered Pitt and Pitt, who at the time sucked at Basketball, said yes. The whole Eastern Conference fell apart. Rutgers got nothing while Pitt became a power house in basketball.
3rd invite:
With the eastern independents were making plans to form a super conference and rumors of the Big Ten expanding to 12 floating around. The Big East was once again were scared that they would lose Cuse, Boston College and now Pitt and maybe Nova and Uconn later on if they ever went to FBS. So they decided to sponsor football in order to keep Cuse, Boston College and Pitt happy and in the Big East. The Big East only wanted to invite more schools for football ONLY. Rutgers tried to get into the Big Ten, but it seem that it wasn't going to happen. So when the Big East invited them for football only, they accepted. The Big East only invited other schools that were suppose to be in that super conference, which killed that idea as well.
Of course, the Big East would later give these schools full membership, regret it, tried ship the football part to the ACC... TWICE. Got raided by the ACC later, twice. Under minded Rutgers and the football schools every chance they got. the whole thing broke up and became two different conferences. Rutgers ended up in the Big Ten anyway with Penn State, so it all worked out in the end.