I was at an Apple Store.
A guy, rather young, brought in his iPhone 4/4S, the screen was thrashed. He was pissed. In his hand, was the phone and the charger (green dot) that was blackened. He said, while laying in bed, the phone and charger started to smoke, may have caught fire, I don't recall. The Genius was rather noncommittal about the issue. He said, with the screen thrashed as it was, it's nearly impossible to tell if the damage caused the issue or not. Also they asked him if there was any damage to personal property.
They flat out said from the very beginning, no matter what, they were going to send him home with a new charger, but he refused it, because the phone seemed dead. The Genius acted as if there was little he could do. However, the manager did come out. The guy did not have to ask for him. They looked at the phone at the bar, and gave him a replacement 4/4S, and new charger. I do not know the exchange of words, or any deals mentioned, just what I saw.
He was pretty happy, leaving the store.
I mentioned to the person sitting next to me, how lucky can a guy get? The response was, Apple will take good care of you, if you phone catches on fire. He made it sounded as if I was the one out of place with my comment.
So, OP, if you were turned away by the store, a Genius, then you were talking to the wrong person.
The notion that a KP could cause a phone to melt and/or catch fire, is ABSURD.
I won't doubt that your phone did or didn't smoke, melt or catch fire, I just think that this is one thing that shouldn't happen. There should be control circuitry such that if certain conditions are met, and a fire could result, all power is shut off immediately. It's a UL safety issue. Can you imagine if someone's house burnt down and a person, even a child were to die from that event, from a phone that went haywire?
I wouldn't be here posting to the forum. I would have my ass down at the Apple Store and camp there until the issue is taken care of. It's not like it was a small wee little accident. It was a potential life treating event.
It doesn't matter who makes what. "S@#T" happens. Some things just aren't a warranty issue. They fall outside of deals and agreements. It becomes a honor issue. It's public relations.
I am sure they won't upgrade you, but they don't have to. But at minimum, replace the phone, charger and cable.
Don't give up anything though, until you are made whole.
After you are satisfied, then let them have whatever you got. They can examine it and determine truly what happened.
BTW: There is a battery replacement program for the iPhone 5. Early batches are bad, and I had my battery replaced. It's like new. They said if the phone is damaged during the replacement, they would give me a new phone anyway. But that didn't happen. My iPhone 5 is a nice little beast. I am very happy with it.