Haha I was also thinking about using an HSM module to sign videos [1]. I think the problem is that anyone can just record a projector screen and replay audio through some speakers, and then Facebook and Twitter will still badge the video as verified and undoctored. You could detect this by analyzing the video and audio, but then it's just an arms race with machine learning.

[1] https://news.ycombinator.com/item?id=18074425