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I think it might not be the most effective use of time to try and figure out the killers' motivations right now, especially since the victims were likely chosen randomly on the first night. However, the commissioner's logic, even if not the best, is understandable. By the way, it's clear that the doctor should have been trying to cure people of their roles today (otherwise, he wouldn't have been able to do it again). Therefore, the only logical conclusion is that the cop blocked him, and now the cop knows who he is.