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.

"As a general matter, copyright infringement occurs when a copyrighted work is reproduced, distributed, performed, publicly displayed, or made into a derivative work without the permission of the copyright owner." https://www.copyright.gov/help/faq/faq-definitions.html

See also a useful FAQ-style article, especially Myth #4: https://www.americanbar.org/groups/intellectual_property_law...

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> I guess it’s difficult for me to wrap my head around how there could be infringement without the (intentional?) misappropriation of the work.

Intent isn't a factor in determining whether infringement exists (as opposed to whether a fair-use defense is available). "The U.S. Copyright Act is a strict liability statute. In other words, following a “rule” that you believe to be true but which turns out to be a myth will not excuse you from liability for infringement. Under certain circumstances, it is possible to plead “innocent infringement,” but even that only serves to reduce the amount of damages you may owe and does not excuse your infringement." (From the ABA "Myths" article cited above.)