I believe that the wobble comes from the wider tolerances in fit between the ball bearings and the races inside the freewheel. If you disassemble a freewheel, you will find some spacers under the lock ring. These vary in thickness from freewheel to freewheel because of those wide tolerances, and are intended to take up the bearing preload. However, there will continue to be movement or wobble as described as the wheel rotates because in the production line process, it's unlikely that the exact combination of spacers will be fitted. You've got to remember that these days, freewheels are near the bottom of the retail pond... as borne out by their cheap price... and hence fine tolerances aren't a major concern.
You can believe the shifting theory if you wish. I don't think it's correct.
The wobble is nothing to worry about, and is mentioned frequently on this forum by people relatively new to bicycle mechanics.