No change in the law is necessary; it's already fair use.
Compare https://www.courtlistener.com/recap/gov.uscourts.mad.220892/... :
> Monsarrat raises a copyright infringement claim against Newman involving the republication of a comment he originally posted in the Davis Square LiveJournal community in 2010
> Newman contends that Monsarrat has failed to state an actionable claim because the allegations in the FAC establish his entitlement to a fair use defense.
> The Copyright Act codifies four non-exclusive factors relevant to the fair use inquiry:
> (1) the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
> (2) the nature of the copyrighted work;
> (3) the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
> (4) the effect of the use upon the potential market for or value of the copyrighted work.
> drawing all reasonable inferences in Monsarrat’s favor, the court agrees that the FAC establishes Newman’s entitlement to a fair use defense as a matter of law.
> As to the first factor, it is clear from the face of the FAC [...], that Newman did not publish the copyrighted post for the same purposes for which Monsarrat initially created it.
> Monsarrat submitted the original post to highlight LiveJournal’s harassment policy and demand deletion of other posts on the community website which he viewed as violative. The Dreamwidth reproduction, on the other hand, was created solely for historical and preservationist purposes. See Bill Graham Archives v. Dorling Kindersley Ltd., [...] (finding that the use of concert posters in a book on the history of the Grateful Dead served a different purpose than the original purpose of "artistic expression and promotion" because defendant used the concert posters "as historical artifacts to document and represent the actual occurrence of Grateful Dead concert events"); Stern v. Does, [...] (finding that defendants’ forwarding by email of a copyrighted post “conveyed the fact of the post rather than its underlying message” and “thus had a substantially different purpose than the post itself”)
> Turning to the second factor, the “nature of the copyrighted work,” the balance again tips in Newman’s favor. The post largely repeats the LiveJournal harassment policy, a factual matter
> The third factor, "the amount and substantiality of the portion used in relation to the copyrighted work as a whole," "focus[es] upon whether the extent of... copying is consistent with or more than necessary to further the purpose and character of the use."
> see also Haberman, [...] ("[I]t has long been recognized that a commentator may fairly reproduce as much of the original, copyrighted work as is necessary to his proper purpose.").
> This factor is neutral. Newman copied Monsarrat’s post in full, but a full reproduction is consistent with historical and preservationist purposes.
> Finally, the fourth factor, "the effect of the use upon the potential market for or value of the copyrighted work" – "the single most important element of fair use," Harper & Row, [...] – weighs against Monsarrat. There is no plausible market for the copyrighted post and thus no likelihood that Newman’s reproduction could have any harmful market consequences.
Applying that to the case of a police officer playing copyrighted music into a livestream of police officer behavior, it is obvious that the first factor ("transformative use") favors the streamer, who is both documenting and commenting on the behavior of the police; the second factor favors the copyright owner ("music sold commercially"); the third factor may range from neutrality to favoring the streamer, depending on how much music the police officer chooses to play -- in the example here, the streamer is favored -- and the fourth factor favors the copyright owner.
However, there is a compelling case that, no matter how much music the officer plays, that is the appropriate amount for the streamer to record -- first, the purpose of documenting what the police are doing is not served by censoring what they do, but additionally, the more egregious the copying, the more noteworthy the officer's behavior is.
Furthermore, while it is possible that a video of police behavior in which everyone is respectfully silent while Santeria plays might substitute for other means of consuming the song, it is extremely unlikely, which trivializes the impact of the fourth factor. Here ( https://www.youtube.com/watch?v=k3ZeUL4fRyk ) is a YouTube video consisting of the song played over a background of the album art. And here ( https://www.youtube.com/watch?v=AEYN5w4T_aM ) is another YouTube video, from "TheofficialSublime", of the official music video of the song. It is not plausible that consumers seeking to consume the song for enjoyment would prefer the cop video to either of those, or even that they might be more likely to find the cop video.