I think what the OP and dermatologist are referring to is exfoliation on the level at which someone would actually pay for or that is sufficient enough to cause obvious outward appearance change. Say an exfoliating product, spa or dermatologist. Something “measurable” so to speak. I’m sure if you break it down to the technical level of whether or not skin cells are being removed by the brush, yes, technically it would be considered exfoliating. But in much the same way as running a dry towel over your face. Let’s not forget, exfoliation in terms of what we’re referring to, is a cosmetic procedure. Its purpose is simply to remove enough dead skin to visibly improve the look and feel of our skin. The only way this is done is with friction or some kind of stripping chemical; hence why all exfoliating products contain some kind of abrasive material or caustic chemical. Shave soap by nature is made to eliminate friction so it makes perfect sense that by dousing even an abrasive brush in slick lather, it’s going to almost entirely eliminate the exfoliating properties of the brush. Which is most likely why the OP’s dermatologist laughed at the idea of brush lathering being exfoliating.