But to the extent US law applies and the other required details of the DMCA safe harbor are attended to, I do think the DMCA prevents the service provider from monetary liability in this scenario. Of course, criticizing them for acting rashly remains 100% fair game.
(As to the question of whether US law applies: one example you were discussing, Hetzner, is based in Germany and not the US. But I can imagine circumstances where US law might sometimes apply to them anyway, and/or Germany might have similar laws. I'm not an expert on the international angle here, and I'm not a lawyer in any case.)