Most music is under a copyright that explicitely prevents public diffusion without a license. Unless the music doesn't have such a limitation, or the police have a license, yes, playing music in a public fashion like that is most probably illegal

it has a chilling effect on a citizen documenting an interaction where the other party has all the power.

There are definitely cases where playing music violates the license, but I wouldn't call it illegal[1]. Playing music at some business almost certainly is not allowed by default, you'd probably need to get a permission from someone authorized to give you one (i.e. a different license). Playing music in public likely has similar rules.

[1] IANAL, etc, etc.

Intent matters. In some situations, yes, playing music is illegal.

Are you arguing that the police should be able to play copyrighted music to circumvent the lawful dissemination of recordings of their behavior?

Of course not.