Problem is that broadly speaking, you would only sign the stuff you want to sign.
Imagine you had a president that slapped a toddler, and there was a phone video of it from the parents. The white house isn't about to sign that video, because why would they want to? Should the journalists discard it because it doesn't carry the official White House blessing?
It would limit the ability for someone to deep fake an official edit of a press briefing, but again, what if he says something damning, and the 'official' footage edits it out, would the press discard their own recordings because they can't get it signed, and therefore not credible?
That's the fundamental challenge in this sort of proposal, it only allows people to endorse what they would have wanted to endorse in the first place, and offers no mechanism to prove/disprove third party sources that are the only ones likely to carry negative impressions.