You have no way to prove the bend wasn't caused by you or someone else or it happened somehow by accident.
Bends in iPad chassis/back housings do not magically happen by itself.
Especially on a such a small aluminum housing/chassis that is for an iPad Mini!
That iPad Mini got bent somehow that you cannot prove!
The standard free, one-year, limited, AppleCare warranty does NOT support any iPad damage caused by the user.
For that type of warranty coverage, you needed to purchase Apple's extended AppleCare+ warranty plan.
One more choice to try.
Try contacting/reaching out to Apple Product support and services about this issue.
Tap on the first link below and scroll down some to get to the Apple Product Support section and phone numbers for your location/region.
https://www.apple.com/contact/
OR
https://support.apple.com/en-us/HT201232
If you need to, if initial 1st tier Apple customer support is of no help to you, you can calmly ask to have this issue escalated up to more responsible, senior level Apple customer support employees to see if they can come up with other possible advice/solutions to this iPad bend issues, but I make no guarantees, whatsoever.
If need be, you can have your iPad issues escalated all the way up the chain to Apple engineering level customer phone support.
Even if no acceptable resolution, Apple, AT LEAST, logs all support calls and issues.
Sorry & Best of Luck to You!