You're right...so here's the logical space:
A. Video/audio/text of/by person, signed, we have knowledge that this video bears their signature, they endorse it
B. Unsigned
B1. Unsigned because it's not them
B2. Unsigned because they don't want it to be associated with them
I think this is still a better state of affairs because we can verify positive endorsements as genuine or not.
You're right, we couldn't verify stuff they refused to sign, but!
Imagine the state coerces people to carry small devices with radio transmitters that constantly transmit, over the length of a second, a signed key, ad infinitum; that way no one can plausibly deny that it wasn't them (unless someone plants the persons device on an imposter).