This isn't a new problem with video, but a new twist on an old problem: manufactured evidence.

One way that courts deal with it is enhanced scrutiny on disputed evidence. Like, if you show up to a court with a document that you claimed someone signed, and they claim they didn't sign it, then the court can keep digging until they figure out who is lying. They can look for witnesses. They can subpoena records from internet companies that may have been involved in a digital transmission of that document. And so on. It's still possibly to lie to courts and manufacture evidence, but most people are not going to cover their tracks well enough to do so without getting caught if the full force the court's scrutiny is turned on them.

And the court finding out you lied to it is very very bad for whatever case you were trying to make.