Oh yes, the All Sports Band were all too real. There used to be a YouTube clip of them playing Solid Gold. The song was "Jet Set." It was a "rock" number, sort of. The excellent Roctober zine had an interview with their bassist (the football player):
http://www.roctober.com/roctober/roc37.html. You have to get the print version, but it's well worth it. Unlike the lead singer, he sounds like a level-headed guy. It's obvious he was a career musician who was willing to go along with the gimmick for the money. Sadly for him, none was forthcoming.
(As a side note, I did weekly shows on WRSU between 1985 and 1992, and I never came across the All Sports Band's LP. Probably for the best.)