It is difficult to give legal advice in a forum without knowing any details, which is why we do not give such advice here. If you are in doubt, ask a review as they mentioned, or ask a local lawyer with knowledge of this specific subject.

What I found interesting though is their wording "either remove the violating content (...) or remove the ad code from the violating pages" which I interpret as: "We don't care if you violate copyright rules and you can keep the illegal content on your site. As long as you don't associate the illegal content with our ads, we are happy to show ads on non-violating pages on your site".

If you copied someones else's work, put it on your site without permission and have now removed the content, then you have done the right thing. Except that you've only done the right thing because you got caught.

Removal is the correction required. Sadly, you've also joined g's database of infringers and potential infringers, which means fine tooth comb applied from here on out. Humans might forgive and forget, but g's AI never will.

How did you get this notification? Within AdSense or via email? Was this a copy of Google content?

You should comply with DMCA (within the USA) but the request must come from the copyright owner or legal representative of the copyright owner. I am trying to understand how the AdSense team got involved in this...

Obviously, the AdSense team has enough power to request you modify/remove your content to abide by their T&Cs but it's a worry when a company get involved in copyright disputes and they are not the original content owners, hosting provider or the publisher.