This issue is often talked about as an unsolvable problem, but I feel like we already have the technology to deal with it.
Lots of devices, such as an iPhone already have a secure enclave that can be used for identity. Why not use this to sign videos and images for authentication purposes?
Then certain devices can produce verified, undoctored images and videos. Or even allow some amount of limited tweaking, and editing while attesting to the original.
This could be embedded into the file produced, like exif data, and read by services like Facebook and Twitter to badge the image/video as verified and undoctored. This could improve the amature case significantly.
Professional photography and video equipment could have similar capabilities so originals could be produced and proven to be genuine.
I guess this idea still depends on the hardware devices remaining secure, which is far from trivial, but it does increase the cost of producing a fake. And to keep producing really good fakes, you have to have a zero day to fake a genuine signature, or it becomes know that any media produced with that device version is suspect.
If such a system became widly adopted, at the very least, savvy users, and the media would be suspect of anything not signed. And perhaps the general public would also learn to be skeptical, particularly if the issue of fakes became more widespread.