The onus of proof is on the copyright holders, the current system puts the burden on the content creators to dispute and prove they have permission. A better system would be one where a ContentID system can flag a video to the copyright holder. At this point the owner must review the video to establish if they believe a breach has occurred, and only then should YouTube block a video or remove its revenue. This must also be backed up with an appeal process that is independently run.
It requires a lot more effort on the part of the copyright holder, but that's how the law works! These ContentID companies will have to actually earn their money instead of leaving it all to a computer algorithm.