For something to be a trade secret, you have to actually keep it secret. If I get the ingredients of Coca-cola from an ex-employee, I've stolen a trade secret. If I work it out by doing a chemical analysis, I've stolen nothing.

There is a difference with anthropic, as no-one signs a licence agreement to buy a coke. But Anthropic are also not saying you can't publish the output of their models. It's not clear to me if trade secret law will (or should) cover a secret which can be extracted from information that licensees are not restricted from publishing.