Personally a brush biopsy is a brush biopsy - name aside. That said the issue is this; it takes the surface ONLY. So you may have some dead skin, maybe some fungus - possibly inflammation, but it's what's underneath that may make a difference. My first biopsy came back inflamed tissue (and that was a surgical biopsy). The entire underside of my tongue was red, inflamed and painful but there was no indication of an ulcer or anything. The tumor was inside my tongue. Now it's unlikely this is the case with you as it is painless for you therefore anything going on is likely to be superficial. However. I would do as he says, get the results if they are negative for cancer, then keep an eye on the area, and if it changes go back immediately - if not do the follow up after three months. If you are still concerned after the results go for the punch biopsy on the second.
hugs and hopefully it's nothing.