I reflected on this myself recently. Model distillation seems to be at least as fair a use as distilling a book.
> Ownership of content. As between you and OpenAI, and to the extent permitted by applicable law, you (a) retain your ownership rights in Input and (b) own the Output. We hereby assign to you all our right, title, and interest, if any, in and to Output.
https://openai.com/policies/terms-of-use/
> As between the parties and to the extent permitted by applicable law, Anthropic agrees that Customer (a) retains all rights to its Inputs, and (b) owns its Outputs. Anthropic disclaims any rights it receives to the Customer Content under these Terms. Subject to Customer’s compliance with these Terms, Anthropic hereby assigns to Customer its right, title and interest (if any) in and to Outputs.
https://www.anthropic.com/legal/commercial-terms
Obviously there is some bad behavior going on in the distillation scene with gray-market token resellers but that is "just" normal fraud.
> to the extent permitted by applicable law, you (a) retain your ownership rights in Input and (b) own the Output
If the argument is that the model itself is under copyright protection then "as permitted by applicable law" would be doing some heavy lifting. Assuming that were true, given that locally-run LLMs exist, what would be illegal: the distillation itself or the provision of service of the distilled model?