It seems more likely that this is just the consequence of training over up-to-date websites (which would include plenty of discussions about LLMs, and particularly ChatGPT). Claude is probably conflating its own identity.
If you suppress tokens “OpenAI”, “Microsoft”, and “Google”, GPT-4 will tell you that it is Project December, a language modeling project to duplicate the deceased based on text history.
It’s just whatever’s close in the latent space. https://projectdecember.net/