That's possible only if they use the same tokens. Which likely requires they share the same tokenizer. Not sure that's the case here, R1 was built on OpenAI closed model's output.
That was an (as far as I can tell) unsubstantiated claim made by OpenAI. It doesn’t even make sense, as o1’s reasoning traces are not provided to the user.
One reason to believe OpenAI here is that R1 will occasionally claim to be made by OpenAI, which in e.g. LLaMA finetunes is indicative of using synthetic data generated by ChatGPT.
Note that this isn't necessarily o1. While o1 is specifically trained to do CoT, you can also make 4o etc produce it with the appropriate prompts, and then train on that output.