Ivan
Very sorry to hear of your troubles...

If you have any issues with the insurance adjuster accepting items and agreeing to pay for them hire an advocate. If that means an attorney, whatever. Insurance companies keep their costs down by denying everything they can.

Fraud is rampant and that is clearly an issue to them, but there is no reason for you to not get what you pay for. I have acted as advocate for a few folks when the insurers tried to be weasels. Surprisingly little pressure is required to make them straighten out... At least in my experience.
art