I was accused of using profanity to an employee at a roller rink when I never called her names. The owners daughter told me “You’re banned forever!” Can I still show up if she’s not the owner?
The rink is private property; they can let who they like in, and they can refuse entry to who they like. They can ban you for any or no reason. (The only exception to this is that they can't refuse entry because of some protected characteristic like race or gender.)
The owner doesn't have to personally issue a ban; any person they authorize can do so. (Consider the case where the owner is something like the Disney Corporation; bans aren't going to be issued by the board of Disney - they will be delegated to the local manager, and probably the shift leader).
You can still show up of course, but you are quite likely to be thrown out.