It should be noted, as I think this is important, if you paid $1000 for the skimmer, the company is not getting a $1000 check from UPS. I've done a handful of claims (as the shipper) with UPS. When it comes to damage, UPS will pay them the lesser of the replacement or repair cost.
Keep in mind, the replacement cost is not $1000. If you bought this from a retailer, it would be their cost to buy a new one from their supplier, so maybe $700. You bought it from the manufacturer, so their cost is, let's call it $500. However, you made it sound like it just needs a new lid and some screws, meaning the repair cost is, what, $50?
With those assumptions in mind, they're not going to get $1000. They're going to get $50 for some new screws, a lid and any other odds and ends (ie, does it need a new box? did you return the manual etc?). Even if they convince UPS that it was a total loss, they're only going to recoup what they would actually be out by throwing it away.
They also require a ton of documentation. It's more than just pictures. They not just that you tell them what the actual cost was, but send them copies of proof. For a reseller, it's as simple as sending in a copy of the invoice. For a manufacturer, I'm sure it's harder.
Also, I could be mistaken about this part, if they pay you for a replacement, they may have the option of requiring you to turn the damaged one over to them, since they essentially bought it from you (and they probably want to prevent people from saying something isn't repairable when it is).
Anyway, long story short, UPS isn't writing them a check for $1000 and if this place is anything like my place, if they feel like you're attempting to cheat them out of something they'll either refuse to do business with you going forward or keep a very close eye on future transactions.