So I recently received an iPhone 5S with terrible body damage (the phone is destroyed from ringer switch up). It was assumed ...
It might just be bad luck, but the left screw on the home button backing would not budge and I ended up stripping it. I just had to order a new home button & bracket, fortunately. I also experienced the inverse, where the screw wells of the new screen on another phone did not hold the screws down. I wouldn't encourage you to try this at home, but a little super glue can go a long way!