Based on your response, and the parent comment, it seems like content hosts have a responsibility: to determine if a DMCA takedown request is valid. If a host doesn't see this as a responsibility, and simply complies with every DMCA (whether valid, invalid, or even fraudulent), I'd agree with op... the host is culpable whenever they comply with an invalid or fraudulent DMCA request. Maybe not culpable in a legal sense, but certainly they are to blame (otherwise who?) for complying with invalid DMCA.
They don't have a responsibility except in a goodwill sense.
The DMCA gives hosts an option to have legal immunity for each specific case of infringement, to gain the immunity they need only take the content down at the cost of outraging a potential customer. They don't have to take the option, however.
It is common in industry for hosts to simply discard obviously invalid complaints particularly if the target is high profile. The legal immunity isn't very valuable if the complaint is baseless-- (sure, there might be frivolous litigation, but that is always possible).
It also seems pretty common for hosts to allow the target of the complaint to counter-notice in advance of taking the material down and then just skip the takedown, or they take it down but restore it immediately on counter-notice (youtube itself does this, or at least did when I was hit with a spurious dmca complaint there years ago). Both of these procedures don't follow the letter of the law and arguably cost the provider their safe-harbour. OTOH, almost no DMCA complaints are actually valid per the specific requirements of the statute, so maybe they don't actually lose their safe-harbour.
I once worked for a business that got a DMCA request for taking down a legitimate site, from a law firm acting on the site owner's behalf. They refused to listen to reason and didn't stop until we got the site owner to call their own lawyers and tell them back off. Luckily, we were outside the jurisdiction of the DMCA so we had the option of simply saying no.
I can't imagine it was the only time such a thing happened, and that alone is an argument for simply ignoring those take-down requests if possible.
