I may well be reading the original post wrong, but I don't think the problem is wanting the phone replaced because of cosmetic problems. It's that Apple is using cosmetic problems as an excuse not to fix/replace phones that have real hardware issues.
Would a single report start an investigation? In all likelihood, no. But reports do get logged and it is possible for an investigation to happen if they get enough with a common theme.
I was on the phone with Apple and AT&T for over 12 hours a little over a week ago. No one wanted to claim fault for my phone arriving bent. After all that time I was told to file a claim with FedEx. I told them if I was going to file anything at that point, it would be with the Florida Consumer Board.
Instantaneously I was informed I could exchange my phone at the Apple store of my choice.
Finally!! Someone is reading the original post correctly.