Does AppleCare cover cosmetic damage?

Trying to get some clarity here. Three months ago I purchased an iPhone 15 pro from a flagship Apple Store in Shanghai. I bought it with AppleCare because of the obvious cost of repairs. I bought a silicone case and the Belkin screen protector as well. A few days ago I dropped the phone onto a hard floor. This smashed the belkin screen protector and damaged the corner of the bezel. The corner is bent and now jagged. This despite the silicon case. Functionally the phone works, visually it looks like its years old and is clearly damaged.

I took this phone back to the Apple Store and was very quickly told that AppleCare would not replace anything that was only cosmetic. The manager being typically Apple rude. So I pushed this and said I have previously replaced an iPad that had a scratched screen but worked. So why would AppleCare not cover this damage? The statement was that AppleCare only covers functions. To which I responded that if I threw the phone on the floor in front of her and destroyed would they replace it. The answer was they would repair only the parts necessary for it to function. if the frame / bezel is damaged and it does not affect the use of the phone it is not covered.

My question to the community is: Is this the same position adopted by Apple world wide? Given that the AppleCare warranty is supposedly global.

[Re-Titled by Moderator]