If I recall, this is basically the surest way to lose your DMCA protection. The key is for them to prove that you knowingly profited from the copyright infringement. Another issue is what percentage of your service is legit/infringing.
As much as people hated it at the time, the DMCA is a pretty reasonable law (which is why the bad guys at various companies are trying to replace it).
The DMCA has no such consideration of profiting from infringement or the percentage of the service that is legitimate versus infringing. A service that contains nothing but infringing content, and puts ads on every page hosting that content, can be completely free from liability for the infringement. No need to speculate based on bits and pieces you think you've heard places -- read the bill! It's short, it's not hard to read, and it's something you should know given your profession.
This is common and incorrect view of the legal system in the US. The law as it is written is only half of the picture. You need to understand the relevant case law to have any idea how a judge might actually rule on a given case. This is one reason why attorneys make so much money.
As much as people hated it at the time, the DMCA is a pretty reasonable law (which is why the bad guys at various companies are trying to replace it).