Right, so it seems that distilling an AI model is legal too then. At least it is somewhat similar.
It is a violation of their terms of service.
There are plenty of good reasons to not use Anthropic's services. If you don't like their terms of service, do stop using them! I personally think Anthropic's increasingly successful attempts at regulatory capture are even more distasteful.
Legal vs "They aren't going to let you do it with their service" are two different things.