I think you're mixing up "weight moving to the front" and "mass moving to the front" a bit. If you lift mid-corner, "weight" moves to the front, but "mass" certainly doesn't move at all, in the sense that the CoG is still at the same place in your body frame. You get increased load in the front, but zero increased mass there, so lifting mid-corner creates oversteer considering only this increased load, with or without load sensitivity.
Only with severe load sensitivity, the available grip doesn't rise as quickly as load does, and you get less oversteer from lifting. But you still get oversteer, not understeer. To get understeer when lifting you'll look at other sources, like coast locking on the differential.
Personally, I think the whole "weight" shifting, "weight" distribution, "weight" this and that, is really lousy terminology. It makes you think there's mass flowing around the car when there isn't. "Dynamic loads" would be much better.