I do not think it is obvious that they F***ed up, I think it is a situation of "prove it" since the owner of the vehicle removed the screws installed by the salesman, and installed a license plate at a different time.
How can the owner of the vehicle prove he didn't install the wrong screws?
How can the dealership prove they installed the correct screws to begin with?
Neither can prove anything, so the dealer will obviously deny it because it will cost them a good chunk of free labor.
I think the owner of the vehicle needs to raise hell to the correct people at Toyota until the dealership fixes the rear window.