What you should be worried about isn't the many, but the few. As usual. Presidents, judges, party nomination committees etc. being fooled by fake private evidence. It's much easier to fool a few people, especially with evidence they can't examine too closely "for security reasons" or some other pretext.
If you've convinced people to look at private evidence, you've halfway there to fooling them already. And sometimes, they're happy to be fooled, because they really wanted to believe what the fake evidence pushes anyway.