If you later recover an item that you've successfully claimed an insurance claim against, you would just have to hand over the item to your insurance company (who might not even want it at that point). And you should have been able to successfully claim the laptop since at the airport, it was most definitely lost and/or stolen.

Also, how can you even assess that the laptop has no physical damage? They can't boot into the OS and can't see that the laptop is in fact completely physically intact. What if the other party broke the webcam or one of the USB ports?