Actually that’s not nuts that’s what’s known as mechanical license. You were broadcasting a cover performance of copyrighted material. Unless you obtained a mechanical license to do that you are not allowed to do that. It’s not an issue of fair use and it doesn’t matter if the band has paid to cover the song or is exempt from it.
Rights compliance is legit hard. I work with churches who spend a lot of time and money to have the proper licenses for the media they use in the venues it’s used in (live/streaming/remote/etc).
On the other side I know songwriters who derive part of their income from the licensing of their work.
