False.

The DMCA act is readable; read it.

Effectively, all it does is offer safe harbor for an ISP, with ISP loosely defined.

Congress attempts to offers a pseudo mediation framework to limit/remove liability from the ISP for the acts of its users.

If the ISP complies with the DMCA, the ISP is immune from liability for copyright infringement.

Here's the part the ignorant ignore:

If the target of a DMCA notice sends a COUNTER-NOTICE, the ISP will/must/should put their stuff , else the ISP can be liable for taking it down without case.

Read the DMCA, it's fairly short as these things go.

http://www.copyright.gov/legislation/dmca.pdf

Disclosure: I spent $80k on attorneys defending against a nuisance lawsuit and used the DMCA as a shield.