That literally is the definition of "public performance." He is in public, playing for an audience that is not his private close family and friends.
> By your logic, if someone is playing music in a park or beach, I could start filming them and they'd have to turn it off. Obviously that is ridiculous.
You can't perform publicly without the copyright holder's permission regardless of whether someone is filming you. You have to turn it off anyway, recording or not. I agree that this is a ridiculous part of copyright law and should not exist. I'm leveraging the system we have here to fight oppression.
The fact that he plays it knowing that it is being filmed for broadcast is what adds the "willful" piece to the already "infringement" piece of the public performance.
I'm not making a normative argument here - copyright law in the US is asinine and needs major reform. I'm just combing through this like a determined prosecutor/RIAA goon would, looking for the right charge.