I think you may be confused here. Anthropic isn't going after users here at all, they essentially told another company that is interfacing with Anthropic's service in a way that violates Anthropic's TOS to "please stop or else we might have to take legal action in the future".

More broadly, you do not need to establish any kind of contractual right to "go after" anyone legally, that's not how civil law works. A cease and desist letter isn't even really legal action, it's a threat of legal action, but even then, Anthropic doesn't need your permission to sue you, just like you don't need Anthropic's permission to sue them.

If you think that inside the U.S., you have some kind of legal immunity to or protection from cease and desist letters or lawsuits from any company, for any reason¹, you would largely be mistaken. If this is important to you, you might want to talk to a lawyer.

¹ Some states have anti-SLAPP statutes that offer limited protections in certain context, but this isn't applicable in the context of this example between Anthropic and AnomalyCo.

My understanding is that, if you directly assist someone violate a ToS, you can be held liable.

Bad analogy but the getaway driver doesn’t need to enter the bank to be guilty in the robbery.