LLMs are hopelessly confused about which model they are. Ask DeepSeek V4 Flash which model it is, and it's 50/50 between "I am DeepSeek (深度求索)" and "I am part of the GPT-4 series developed by OpenAI." Ask Claude, it'll say Claude. Ask Claude in Chinese, it'll sometimes say DeepSeek.

It's incredibly funny, but I don't know whether it's related to distillation; it's probably quite rare for a distilled trace to mention which model it came from. (I'm not saying distillation doesn't happen, just that it's possibly unrelated.)

For your specific example, the internet is full of "As a large language model developed by OpenAI, I can't..." due to people pasting chatbot output without reading it. Seems reasonable for that to surface as part of the CoT for your question about model capabilities.