Technically speaking, the NCAA ban does not include the BET, that was separate. The Big East ruled that any school on a postseason ban in any sport is banned from the Big East Tournament. Other conferences have made similar rulings before, such as USC being banned from the Pac-12 title game in football last year. That was the Pac-12's decision, not the NCAA's. Ohio State and Penn State are likewise banned from the Big 10 title game this year via Big 10 ruling, not NCAA ruling, although the Nittany Lions hadn't been banned yet when we were.
And there is even precedent in basketball, albeit not in large conferences - a couple years ago when Binghamton was banned from the NCAA Tournament, the America East Conference banned them. Come to think of it, USC was banned from the Pac-10 Tournament in 2010 as part of their postseason ban. That was the Pac-10's decision, although they already had the rule in place.
Bottom line is, the NCAA banned us from all their tournaments, NCAA, NIT, CBI, and CIT, but not the BET. They do not have the authority to do that. However, the Big East would forfeit their autobid if we won, by rule. Most conferences already had rules banning banned teams from conference tournaments. The Big East, for whatever reason, did not, but now they do. Honestly, I'm surprised it took them so long. I guess it never mattered before.
However, yes, we are banned from all postseason play. And there already is a Connecticut tournmaent during the regular season (at Mohegan Sun, I believe, actually), featuring everyone in the state but UConn. We're not there because it would be a waste of two or three games for us to be playing in that and it would kill our non-conference SOS, plus I doubt they'd want us anyway since we'd always win.