That is provided the DMCA notifier responds to the follow up request.
They usually don't.
This is how a DMCA farm operates. Company A wants some stuff of the internet. They pay DMCA Spam Farm B a fee, DMCA Spam Farm (backed by a law firm but no actual lawyers are involved) sends a DCMA notice to every site that turns up in their TinEye search. By law, they have to have a way to respond to the request. Now in a high end case there is a human that monitors that email for response, but in this case the system basically logs "we got a response" and ensures they don't renotify that host for the same content (against the law).
The reason no one follows up is because the initial notice has gone through an actual lawyer for legal soundness - you are not opening yourself up to any sort of legal action because of the content. If you RESPOND to the take-down response, that response needs legal review to ensure you aren't doing anything stupid. That takes time and attention and is beyond the capabilities of these take-down farms.
Again, if anyone actually ends up caring, they can follow up. But in most cases, it simply just isn't worth it and the case is binned. "We got 95% of the content down, good enough, mission accomplished".
This the digital equivalent of what was called in the circles I was exposed to as "the scary-gram". Basically if you are in an intractable deadlock on an issue, you get a lawyer - ANY lawyer - to send someone a notice on their legal stationary that legal action is being considered and in 80-90% of cases the person on the other end will capitulate because it isn't worth the hassle to go to court. It doesn't matter if its a real estate dispute and you got a corporate contract law attorney, the notice looks official and people will usually comply.
A lawyer out in a rural area made "pocket money" sending said scary-grams out during hunting season. A few cases the people ignored them, he had one guy actually retain a general practice attorney to fight about it, but in most cases they stopped the objectionable behavior.
I had a dispute with some distant family over some property I owned an interest in. I lived out of state, got a lawyer friend who owed me a favor to reach out to a friend who owed HIM a favor in the state the property was in to send a scary-gram, and while it made the next family reunion a little tense, the dispute was settled for the low cost of $25.
I have been able to observe admins on the other end of such DMCA take-down requests and even a token "We believe we have the right to host this material" is more than the automated systems are willing/able to handle. the other way to ensure you never hear from them again is to request all further service be physical: this requires postage and a legal-document handling service, which is beyond the capabilities of these takedown farms so they usually go away because you simply are not worth the hassle.
in the interests of full honesty: It was a parody/commentary fair use exception in those cases. It might go differently if the response is "we were told we allowed to host this contrent provide proof we are in violation"
