The problem Google has it's that it's not just acting as someone's bank, it's profiting from the content via ads, and that opens up a fair argument of complicity.
I'm not about to judge as to whether that means it deserves to bear all responsibility for content- certainly I think it's unrealistic that it should have to scour all it's servers and make a judgement on whether every bit of content is or isn't there legally, but I don't think it's unreasonable that if someone points it to a specific bit of infringing content, that given that it both hosts the content, and profits from the content, that it should have to take it down, else I don't really see how Google can argue against the suggestion that it's knowingly profiting from illegal content at that point - if it's hosting the content, providing access to the content, and the content is known to be illegal, and it continues to host and provide access to it, then surely it's pretty clear cut that it's intentionally profiting from illegally provided content?
But I think that's the key thing here, it has to be knowingly doing so. That puts the onus on the alleged victim to put the effort it and make it clear to Google that the content is not being legally distributed - and even there Google should have recourse to get the courts to rule if it's not certain and should be protected until the courts have decided, but it most definitely should not put the onus on Google to try and figure out what content is illegal.
Your analogy would be better phrased as someone having stolen money from you, stored it in a bank and the bank is profiting off that cash by investing it, and continues to do so and refuses to hand it over even when it's been made clear to the bank that that money has been obtained illegally. In that case yes, I think the bank absolutely can no longer pay the innocent party - once it's been informed of alleged or proven illegality then it has a responsibility to investigate and act.
As for the demands of $100m? well, that's a different issue - that's just the US' stupid sue everyone for everything culture.
So as for this particular case, if they've given Google specific URLs and Google hasn't acted then apart from their stupid financial demands then I don't think they're really much in the wrong. If they've just blanket told Google to scour every inch of their server and make arbitrary judgements on legality then these folks should be told to go screw themselves or to come back when they have something more concrete.
So all in all, I think this sounds like it's probably a stupid case, but that doesn't mean Google should necessarily be given a get out of jail free card from knowingly profiting from illegally hosted content- there has to be at least some degree of responsibility held by them to act if genuinely and reasonably informed.