The problem with deep fakes is a hostile nation taking over your phone/facetime calls and sounding exactly like your own parents. How can you tell if they can do it in real time? A bad actor could get you to do some really bad things.
That is an interesting point, but this already happens on voice calls. My grandma got a call a while ago from someone claiming to be my brother. Said he needed money because he was in a South American jail or something. Luckily shes still pretty sharp, so she hung up and called my brother (he was not in South America) so the ruse was up. She was pretty shaken up though. A video call would be more convincing but only an incremental, not fundamental, difference.
My mother received a similar call, telling her that I'd had an accident.
If you're thinking such an evil persons should be in jail, don't worry, they are! It's them who are in South American prisons using burners or stolen phones.
There's nothing in that link that contradicts what I wrote. My source was an official police alert. I lost the reference, but here is another one from a newspaper (in Spanish):
Maybe PGP or some other form of cryptographic signing will become (more) mainstream as a result of this. Or at the very least a secret word that families can share amongst eachother to verify identities.
Cryptographic signing just moves the problem from the authenticity of the document to the authenticity of the key.
That can be very useful when it is useful to only have establish trust once but that's not really the problem described here. The secret word is probably more useful in being so simple, however it still has to be established beforehand.