I need help understanding the logic

I did and the depreciated value isn't even close to being able to purchase a new x-box. All I am asking is can I pay to get it fixed or not?

I suggest you (or your parents) take it up with your insurance company and the restoration company as they would presumably be legally liable especially given the non-working state of the console.

Just so you know though insurance companies are evil and give you the "depreciated value" of whatever you insure. They of course are the one's to figure out this "depreciated value" but I've heard many, many horror stories of getting pennies on the dollar
for what it would cost to replace the item.

Sorry once a console is opened by anybody other than MS they will not touch it your only option is to buy a new 360 and for future reference don't post reference numbers on the forums.

Sorry but no, the policy is there because once an unauthorized service is done Microsoft has no way of knowing what has been done to the system. It makes it difficult for them to repair and if they did repair anything they'd be culpable for any damages
done by the unauthorized repair.

It seems--to me--that your only other recourse would be to bring up a civil suit against the insurance company if they refuse to accept responsibility for this. Sadly it would cost you more in court costs to sue them than it would be to buy an Xbox One
let alone a 360.

On the main menu, it refers to your online character. You must load your offline pro to look at stats.