Not sure that's accurate. From something posted on Cisco's website: "Apart from payment for the service, the carrier is absolved from liability regarding the content of the messages, and from the actions of the customers of the service. This form of social contract is the basis for the status of a common carrier."
Actually, no. First, there is some legit content on TPB. Secondly, however (and more importantly, in this context), for an ISP to block content in one illegal case implies (in a legal sense, rather than a technical one) the ability to block it in all such cases, which then exposes them to liability for the illegal content they didn't block.
Effectively, the only sustainable way to maintain common carrier status is to maintain a deliberate ignorance of the legality — or lack thereof — of any traffic they might carry.
http://www.cisco.com/web/about/ac123/ac147/archived_issues/i...
Effectively, common carriers are protected from liability unless they know that what they carry is not legal.