IMHO the person posting the YouTube video with the Taylor Swift song in background would have an excellent shot at a fair-use defense against any claim of infringement of the copyright in the song or the recording (which could be two different things). See, e.g., https://fairuse.stanford.edu/overview/fair-use/four-factors/

I also strongly suspect that the owner of the copyright(s) in question would think very hard before making an infringement claim in the first place, for fear of the adverse publicity.