To be honest, it doesn't matter what they are hosting. The important thing from a legal point of view, is how they respond to DMCA takedown notices. If you have 100 infringing pieces of material on your site and you only get 1 takedown notice, you only have to remove the 1 piece of infringing material.

The law is pretty clear. It's not the webhost or ISPs obligation to police it's own content. That would put the ISP or webhost in the position of having to determine who the copyright owner of every piece of material on their site was. It is the copyright owner's obligation to send a proper DMCA takedown notice when infringing material is found.