IIRC it's the result of an FOIA request

IANAL, but in most cases, body cam video falls is available through a FOIA request. Often times either the media will file a request or a defense attorney, victim, or individual involved in the incident will have access and release the video on their own. Same with dash cam video from police cruisers.

Having worked for a local municipality IT: All the electronic information held by the city is public property. Emails, documents, videos; everything. When asked to release information, they are allowed to redact certain personal data points about citizens (such as SSNs) but they are obliged to release the requested information. This is because the public bought those servers, pays the employees, pays the bills to keep everything running, and therefore owns it all.