Granted, one could argue that this only happened because the API version of Claude doesn't appear to use a system prompt. If that's the case, then the LLM lacks any identity otherwise defined by the initial system prompt, and thus, kind of makes one up.
Nonetheless, point remains, it's kind of interesting to see that in the years since the launch of ChatGPT we're already seeing a tangible impact on publicly available training data. LLMs "know" what ChatGPT is, and may even claim to be it.