Warranty got denied and now being charged $400. Need help asap

So a month or two ago I called to initially make an insurance claim as I do have phone insurance. I explained what happened to my phone (screen came unglued, had not been dropped cracked or anything my fault at all) and the person said it sounds like it would be covered under warranty so I did that. Month later I get my phone and a letter saying im going to be charged $400. They put a sticker on a screw that was missing like that was my fault a screw came out and then the screen came unglued. How do I dispute this because it's ridiculous? I just want to talk to someone higher up and solve this. If that's not possible What else can I do? I hope I don't get "call customer service" response because I have and they do ABSOLUTELY NOTHING. And I'm running out of time because the bill came in the mail and I don't want to have a late payment. Thanks In advance for the help. This is so stressful. Why do you have to do this to me at&t, just why?