The problem is that its algorithmic. The content owners aren't clicking around and claiming videos -- Google's Content ID system finds videos that look similar to theirs and then claims the video.
The ideal case would be someone reposting a trailer or a music video to Youtube. The content is identified as being owned by a partner. Now the partner gets the money and the poster still gets views.
Cases like the OP thus cause a problem: the majority of the content is 3rd party and free.
Note: I'm not defending CID or saying its a good thing. I just think your proposed solution won't fix the issue at hand.
The initial claiming process is automatic. But as noted in the article, the uploader then has an opportunity to dispute the claim. The rights holder is then supposed to manually verify it and either approve or dismiss it. The problem is that there is no penalty for just approving every claim after "reviewing" it. Contrast this to the DMCA process, where after the uploader files a counter claim the rights holder must file a court order in order to keep the material down.
At the moment it's a terribly one-sided process that allows big media companies to profit for absolutely no reason. Fining companies for approving disputed claims in error seems like a pretty good solution.
There's no abuse mentioned in this particular article, and in this article it is exactly a "technologically broken" issue.
The article says that if a TV network's real, legitimately copyrighted feed, that they are correct in telling Youtube is copyrighted uses public domain video in some parts (which doesn't mean their particular feed based on it isn't still copyrighted), then other videos that use the same public domain video (from the original source, not off of the copyrighted feed) are identified as being the copyrighted source.
I mean, fines like $5,000 per false claim.
That will stop abuse of it, real fast.