Distillation is not illegal by every definition of the word.
I am waiting for a precedent on this one. In general, training on copyrighted material is legal, there is a lot of precedent there. But every now and then there is a case where the owner of the training material wins.
I don't remember the details but I believe one of these instances was when one company trained its AI on the knowledge base of another company and turned it into a competing product. Fair use was denied because of that direct competition. Distilling a LLM to make a competing LLM looks kind of like this, or maybe not, I don't know.
It would make sense for distillation to be legal in every way, LLMs are built on a broad interpretation of fair use, but sometimes, law is weird.