It's kind of complicated. Water pressure from on top of the cover CAN force water behind the liner at the seam where the top of the liner meets your coping (the cap or masonry edge of the pool). This would be the worst case scenario.
Let's assume that is happening.
So, by draining all that water off the cover, you reduce the downward/outward pressure of water INSIDE your pool on the walls of your pool. With me?
By adding water to the pool at the same time, you are equalizing the outward water pressure on the pool walls, thereby forcing up and out water that might have been pushed behind the liner at the coping. Still with me?
If the water on the cover is dirty, instead of adding that water to the pool, just rig up a garden hose and add clean water through the skimmer at the same time you drain the cover. That will keep the pressure in equilibrium.
I hope this makes sense. Let us know if you have any questions!