So I took the phone back in this morning. I hadn't left the mall yet so it was pretty quick.
I approached the Genius bar and told them my situation, as well as showed them my papers from the phone swap.
The genius looked at the gouge and told me that it "wasn't that bad" and that there was nothing that they could do about it. He tried to claim that all iPhone 5's have blemishes and that no matter how many phones I tried, they'd all have something like that on them.
I of course told him that was crap, that my previous phone didn't have a scratch on it and that I couldn't accept a damaged unit considering the price they demand for these phones. No luck, he wouldn't budge. I then demanded my old phone back so I could exchange it with Verizon instead (I bought it in a VZW store). They said they couldn't give it back now that the swap had been completed.
By this point I was pretty livid. I'm sure the genius could tell, and he finally said that if I could get verification from VZW that they would exchange, he would try to get my old phone back.
The Verizon store wasn't open yet, so I went out into the concourse and dialed apple's customer service line for guidance. They said that the store needed to make it right, and to insist on speaking with the manager. I went down to verizon and waited for them to open. Sure enough, the manager there said they would exchange my broken phone for a brand new one no questions asked.
So I went back to the Apple store, and insisted to speak with the manager. Manager was only marginally more helpful. He took the damaged replacement phone in the back and must've been gone for about 20 minutes. When he came back he told me that they could give me my old phone back, but that if there was any hitch with Verizon and they ended up not exchanging my phone, Apple couldn't help me anymore. He said they're only letting people swap for cosmetic blemishes once at this point. I laughed because that wasn't even the reason I brought my phone in in the first place. I think it's lame that they are trying to force second rate hand-sets on people when they charge so damn much for them in the first place.
Anyway, Verizon did the exchange with no problem. Unfortunately, they are out of stock in the store at the moment so I am left with no phone while a brand new one is shipped to me from the Verizon warehouse. 2-4 days is what I've been told.
Fingers crossed that this next one actually works, and doesn't look like someone dropped it on the concrete.
Such a shame, I've had such positive experiences with Apple in the past. This one will be the experience that stands out the most though, they've lost a lot of trust from me.