The burden of proof is on the positive claim. Even if I were to make the claim that another human was reasoning I would need to provide justification for that claim. A lot of things look like something but that is not enough to shift the burden of proof.

I don't even necessarily think we disagree on the conclusion. In my opinion, our notion of "reasoning" is so ill-defined this question is kind of meaningless. It is reasoning for some definitions of reasoning, it is not for others. I just don't think your shift of the burden of proof makes sense here.