You don't need a blockchain or proof of work for that, timestamped digital signatures are a thing that's being used already, you just need a proper trust infrastructure.

A blockchain with proof of work solves the problem of decentralization and absence of trust; however, for legal matters, having a centralized root of trust is the simpler way to go and requires much less resources.

However, tampering with the actual recording device is a very relevant risk - I struggle to imagine an attacker who has the desire and capability to make some serious crime, and convincingly fake a video as part of it, but would be foiled because they can't figure out a way to upload it properly in the exact manner as a real camera would.