I had this happen with a package I sent recently. Stragely, the buyer actually lived in what looked like a failry isoluted, rural house (I googled the address, trying to figure out the liklihood of theft after delivery, but they literally had no neighbours and I doubt the road was travelled that often). 

I believed the buyer though - they had contacted AP before ever contacting me, so they already had a case open and Ap wouldn't provide me any real details on the matter because of that, unless the buyer authorised me to access the case details - which they ended up having to do because AP agreed the parcel had not been delivered to them, despite the tracking status, and stated they would send me the refund. (This really surprised me, because I thought for sure the buyer would be the one compensated in this case). The package didn't have insurance or SOD, but was only worth $40 so I got fully reimbursed the value plus postage (I had already replaced the order for the buyer at that stage).

If it helps, I know that people have successfully argued missing package claims that were "safe-dropped", because if it goes missing after delivery, it obviously wasn't safe to leave it. (My buyer actually said they thought their contractor was dodgy in my case, as apparently it wasn't the first time something like this had happened, so she gets stuff sent to her partner's workplace now).