You think people in college football weren't aware of the goings on at Miami before they were in the press? From people that should know a bit about it, the other conferences didn't want them.
Miami actually was invited to the BE in 1990 before the BE had even definitively decided to form a football conference. By the time Miami played in the Cotton Bowl that season, it was decided to form a football conference and they were even wearing Big East Football patches on their uniforms during the bowl game, and then went about embarrassing themselves with over 200 yards in penalties, largely from unsportsmanlike conducts, while beating down UT.
Very public that Miami was trying to follow FSU into the ACC prior to getting their BE invite. They apparently had no other conference options than the BE. For optics like the above bowl game antics and the open-secret, behind the scenes shenanigans, no one wanted to touch them. I wouldn't doubt that FSU didn't want them to come along. Maybe a combination.
All I can tell you that it is some interpretations of how it came together. May not be the completely story. But Miami's reputation did not help itself.