DMCA requires a statement:
"under penalty of perjury, that the complaining party is authorized to act on behalf of the owner of an exclusive right that is allegedly infringed."
The perjury statement is just that the person sending the complaint is an authorized representative of the _alleged_ owner.
In other words, if you or I sent a complaint that someone is violating Bill Clinton's copyright, THAT would violate that section, because we're not authorized to enforce Clinton's rights.
As to the accuracy of the complaint, DMCA provides that you can be sued for actual damages if you KNOWINGLY file a false complaint. "Knowingly" is a special word in law, with a carefully established definition. It means more than recklessly or negligently. To sue them, you have to prove that they KNEW it was bogus. If they filed it without caring whether or not it was bogus, that's insufficient. It would be better if you could sue for reckless or negligent claims, but you can only sue for knowingly false claims. Changing that one word from "knowingly" to "negligently" or "recklessly" would go a long way toward fixing DMCA.
Secondly, the bogus claimant can be sued only for actual damages. Suppose it costs Google $5 to process each takedown. For a knowingly false takedown notice, they can sue to get that $5 back. They're not going to pend $100K to sue someone for $5. Not going to happen. What would fix that would be the same thing that holders of registered copyrights have under the law - statutory damages. The current text of the law is:
Any person who knowingly misrepresents ... shall be liable for any damages ... incurred
We could just change that to:
Any person who RECKLESSLY misrepresents ... shall be liable for the greater of $25,000 or any damages ... incurred.
Any person who negligently misrepresents ... shall be liable for the greater of $10,000 or any damages ... incurred.
A Google lawyer could then sue Warner Bros for 100 reckless notices and damages would be _at_least_ $2.5 million which pays the lawyer's salary for several years. They'd settle for the $1 million "negligent" amount, and Google could have a staff of lawyers suing all the assholes, hitting them for a million dollars each time until they stopped sending notices recklessly.