To some degree I understand the cop's position. The internet is an insanely dangerous echo chamber. The vast, VAST majority of police interactions are not that. The vast majority of police interactions are well-meaning officers maintaining public order. This doesn't excuse the interactions which
are unrighteous and deserve to be exposed, possibly including the interaction that these people were protesting.
The officer here was, to my view, the more sane one. He said you could record. If something happened bad enough to justify publishing the video to expose the interaction, a little Taylor Swift music shouldn't stop that dissemination of information. What it can do is dampen Ambient Outrage; a citizen surveillance state of uploading every police interaction out there to social media for Internet Crazies to get angry about because Cops Are Just Evil, where there is no nuance, no context, just outrage and ad dollars for the protestors behind the uploads.
Its memey and sad that this is the lengths officers have to go to. That's it. But if it works, especially in a situation when the officer flat-out says "yeah you can record, that's fine" (good on him!); I think their underlying rationale is perfectly sound.