Stream, but remember anyone can send a DMCA take down request for the evidence, and big companies have law enforcement liaisons who would be more than happy to remove content at the behest of LE. Some platforms will remove any violent content uploaded by users, so with some rules lawyering from LE posing as another user, it can be taken down.
Would the government even have standing to file a DMCA takedown for anything? Anything the government creates is in the public domain meaning there’s no copyright to infringe.