My understanding of what Anthropic are saying about this is that the labs in question aren't forwarding things to Claude to make money nor even to look better to the customers whose queries they forward to Claude but to get access to conversations between real users and Claude, which they can then use to help train their own models.
(I do not guarantee that I'm understanding right, and still less do I guarantee that what Anthropic say is actually true.)
it's not too far fetched, for example when Deepseek came out with their new caching techniques where they were able to offer those insane discounts, it was only available through their API which would retain and train on your prompts
so, they've been on the record, and very open about it, at least for some of the labs.
(I do not guarantee that I'm understanding right, and still less do I guarantee that what Anthropic say is actually true.)