After that it goes to the courts (if the DMCA complainant chooses to sue).

So, in short, when Congress built the DMCA, they made it possible to silence someone for a guaranteed 10 day period with a spurious DMCA request.

If they'd claimed a copyright infringement, though, the ISP has to act.

How many times have we gone "how the hell did that decision happen?" with a patent or legal case? Seems like it happens daily.

1. The hosting company does not have to act, ever. It just may cause them to be liable.

2. The hosting company can always push back on faulty notices, like this one, with no impact. There is nothing for them to be liable for, as the subject matter is not properly for a DMCA notice, and an invalid DMCA notice imputes no knowledge to them, even if the part that would normally give them notice is valid. This is actually well settled.

So, in short, no.