We use Amazon Buy Shipping, which will cover the items if they show delivered but the customer says they didn't receive it. How do we handle damage claims?

We have some customers claiming "damage" on their package they received. USPS includes $100 insurance, however Amazon is saying we need to refund/replace the item without them sending it back. USPS requires us to show the items in person to get an insurance claim, so we are not able to file an insurance claim for lost/damage when the custom claims they are damaged. The customer needs to file the claim themselves with USPS if they have damage to show proof to USPS (they will ask for in person proof for damage). We asked for some pictures, and the products have a in some cases no visible damage, so its possible the customer is exagerating.

We looked at this one customer in particular this week who requested "replacements" and noted within the past 1 year, Amazon has credited them nearly $600 in orders for us for damage (mixed FBA and self-fulfilled).

So the specific question is here is how do we claim damage with USPS packages when the customer received them, because Amazon is telling us to ship them another (free) product, and we will not be able to file insurance on this.