The search engines (or ISPs) require some proof, but do not make decisions about the legitimacy of the claim. The claim has to at least make sense, e.g. you can provide a URL that you claim is your intellectual property and another URL that you claim is an infringement of your intellectual property, and they can be visited to verify that at least the URLs do exist and that the infringement could exist.
I don't know if it would be better for the ISPs/SEs to require a higher standard of proof than an affidavit. It appears to me they prefer to stay out of the fray and let people duke it out in court.
S.G., you do make a good point about the impact it could have on an online business. If your site is down for a couple of weeks because of a bogus takedown claim, that's going to be a slim month for sales. I suppose one has the option of taking the accuser to court for filing a false DMCA removal request and sue for lost revenue and legal fees, but that's a huge hassle.
I think you are incorrect on your first statement here. ISP's do not require any "proof" all that is required is the take down notice. It is not the ISP's job to determine if there is evidence, proof, or if in fact there was an infringement. Their only requirement is to take down the questionable content, notify the supposed infringer of the take down and notify the complaintant that the infringer was notified. Doing this satisfies the safe harbor provisions.
Now the ISP does have the option to ignore the request, but if they do and the complaint makes it to court, the ISP could also be held accountable for the infringement. I don't know of any ISP's that are going to go out of their way and spend their time looking to see if a claim is legitimate, I know as a hosting provider myself I wouldn't. It's simply not my job, and I'm certainly not in the position to police every one of my hosting accounts.. I get a takedown notice, the content comes down, plain and simple. If someone were to come after me as their hosting provider for damages, they would never win as I only followed the guidelines set out in the law.
Now Go-Daddy is a different beast, they just don't remove the content, they kill the entire hosting account, which in my view is completely over the top, but I think they have that clearly stated in their TOS.
I also think the biggest issue with getting "delisted" within google, would be proving damages, as Moe state it would be a huge hassle, ands you'd have to sue for attorney fees and damages" ie lost income..how many people could actually prove damages?? just because your numbers may be way off isn't going to be proof enough. You'd have to be super anal, like myself to really have a chance at proving this. for example I get at least 4 calls per week from potential clients that find me thur google, I ask every single caller how they found me, and it gets noted in their file, which is created while I'm talking with them that first time. I think it would be a good bet that if I got de-listed from a bogus complaint from a competitor, and I sued them I might win the damages...."Might" and "IF" can be to scary words however..