I don't see what TPM's needed for.

The device hashes the video (trivial on any CPU capable enough to handle media) and uploads that hash, a simple blockchain network (or some sufficient existing blockchain) ingests it and sets the timestamp, then it's stored publicly, unencrypted, but set in stone.

Now that I think about it, this would work for any file (like documents) or indeed anything hashable. It's simply a public ledger of hash + timestamp pairs to prove "a file with this hash existed at this time," and there's no need to encrypt any of it.