Did you ever try to get a license for a "performance" like this? I did, once, just to see how difficult it is.
Turns out that, at the time, neither BMI nor ASCAP had a way to legally play their music unless you were a professional DJ, were pressing at least 200 CDs, or were re-mixing their music.
After 6 weeks of phone calls and emails, and getting shuttled off to various other agencies, it turned out that they had no license that would allow an individual or a business to play songs from their catalog for a single event.
Of course that does not prevent them from suing for lack of the same.