My understanding is that the biggest problem with a stuck mic that it prevents the pilot hearing ATC (making a fool of oneself is a secondary problem).
Hitting the mic to whistle a TV theme-tune over someone else's callsign just seems ... not good. I get that at the end of a heated ATC/pilot exchange a third-party might anonymously throw a "Calm down, sir" into the gap between transmissions (at either ATC or pilot), but this sounds different. Why would anyone think it is OK to interject something into that ATC/pilot exchange?
The entire whistle is, I think, roughly 0:20 to 0:23. Why didn't it impact pilot and ATC trying to use that frequency? Did they really both blow it off?