I don't see how a blockchain helps with problems arising from deepfakes. What's key for the solution is signing the content on the physical device, aka public key cryptography. To my understanding, a blockchain solves the problem of agreeing on a temporal order of events (eg. transactions), which I don't think is critical in the case of deepfakes.

Temporal order is absolutely critical in determining the truth of an event, as deepfakes could be used after the fact to distort the facts and mislead a viewer. Blockchain allows for the use of public key cryptography with a guarantee of the time in which the video/document/etc was created.

If we trust the device manufacturer to only sign genuinely recorded videos, couldn't we also trust them to sign the videos with a correct timestamp?

Where would manufacturers store and display these timestamps? Would each manufacturer host their own proofs, or share a database together? Who would pay for that, indefinitely? The economic reality is that no one would ever pay the costs for such a ledger of all video timestamps. This is where blockchain is necessary.