It is legitimate though. Data is not copyrightable, and even if it were they'd lose the ability to derive that data from other peoples copyrighted works.

At best what you have is a contract violation between the provider and the distiller, and that only applies if the one doing the distillation is the one that entered into the contract with the major LLM provider.

Likely they were smart enough to just not do that. Pay some scrubs on the internet to collect the training data for you. Maybe they violate the TOS, maybe they don't, it doesn't matter to YOU. You didn't have an agreement with OpenAI or Anthropic to violate... And as others have said OpenAI and Anthropic are likely doing the same, which is why ChatGPT sometimes thinks it is Deepseek.