I did not ask the model which model it is, I'm not interested in the model answering the question either. The interesting bit is that this happens while doing another task. I'm not saying that this is because of distillation of openai's model either or a proxying. To me this looks like a side effect of their RL.

Could it be because Claude / ChatGPT are the most viral models and thus are more likely to be in the training set so when someone asks "Which AI are you?" the likeliness of Claude and ChatGPT being a reasonable answer is higher?

That's because every single model release after GPT-3.5 has been, at least in part, been trained on data synthesized by GPT-3.5 and then the other OpenAI models, as well as Anthropic models later.

Also the distillation attacks and other distillation methods that gather chain of thought information from frontier models are also used to generate vast amounts of data in order to generate synthetic datasets to post-train what I believe is the vast majority of models that are being released.

If you look at any information about how these models are trained, the details about how the data has been synthesized, where the agentic traces come from that are used in post-training, etc., they almost never tell you about exactly what model was used to generate them.

All distilled models do this.