Do it basically the same what TLS verification works, sure the browsers would have to add something to the UI to support it, but claiming you can't trust that is dumb because we already use that to trust the site your on is your bank and not some scammer.
Sure not everyone is going to care to check, but the check being there allows people who care to reply back saying the video is faked due to X
The first amendment applies to the government's actions. Not personal actions.
Hate speech is not a protected class so you can be refused service for it at any business,