I know it can happen, I'm just not exactly sure how. I think it only happens when the car you're currently using in GT mode is the one you use in arcade mode. It might also happen when you buy and install tuning parts for the car in arcade mode, not sure though.
Anyway, if you don't do those things I'm 100% it doesn't change your stats. I'm just not sure about what does change it. Maybe someone else knows.