Almost. The suggestion that the der hanger can cause a wheel to shift is not the best way of saying if the dropouts are not parallel to each other AND also not parallel to the centerline off the bike (this part is rarely mentioned) that the wheel can shift on tightening. Technically the hanger is not the axle slot.

I've seen many bikes that when the wheel is tightened in place it wants to "walk" or move slightly within the drop out. I have found this to be far more likely with axle nutted wheels (the axle sometimes wants to turn with the nut allowing that "walking" to happen).

Having read this thread I would want to see the bike and wheel before making any claims of what's wrong. Andy