I think you'd have to claim ownership (ala RIAA) to compel a publisher to remove the recording. The FCC license that airline types are required to have is a license to broadcast on public airwaves.
That said, you can always ask a publisher to remove content, although I don't know of any requirement to do so unless the content was obtained fraudulently.
That crew did an excellent job of not being dragged into the shouting match. I've heard it go a lot worse.
Remember, every time you key the mike - the whole world could be listening.