What do you mean by "burnt-in" exactly? Like a watermark? I don't see any reason why the running timestamp can't be encoded in the file format, invisible to the user. Then tampering would at least require some technical know-how.
Meaning the timestamp is included as pixels in the video frame, it's not metadata. Usually the timestamp also has some alpha, it's not just a black background, so tweaking it would require some skill. This is far from foolproof but it at least raises the bar a little bit.
It can be useful because when you're watching a video where nothing is moving, you know the video hasn't frozen; and if you transcode the video to another format (upload to youtube, for example) the data is preserved.
Of course, even better would be if the cops' cameras recorded to a standard format that included accurate timecodes and secure digital signatures - and that same format could be viewed by most video players.
