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.