There is no real solution to this problem, but my thoughts on the matter are that in the future it will be common for cameras or recording devices to have a cryptographic signing key and the resulting footage would contain a signature. This would allow news outlets to prove to their audiences that the footage is untampered with. It could also be chained so that officially licensed syndicates could also offer provenance to their audiences, or that clips/re-encodes of the same footage could link back to an original recording.
This doesn't stop organisations or individuals from recording a deepfake, but it would put their reputation on the line (similar to how we have certificate authorities signing SSL certificates now).
It's up to you then if you want to trust the footage provided by AP vs. the footage provided by Infowars.