That's an amazing story so thanks for sharing it! They really told you this on the phone? When I've heard people relate GPS dropoff stories in the past the USPS always demanded that you could only get GPS information in-person at the main post office for your zip code. Did you call the national USPS help line, or did you call your local post office directly?
On a related note I have had the tracking from all three major carriers, i.e. FedEx, UPS, and the USPS claim that something was delivered up to an hour before the carrier actually delivered it. My guess for this is that couriers sometimes scan multiple items at once as delivered while sitting in their truck for a block, street, or general area to save scanning time. I first time I had the kind of panic you just described was about 3-4 years ago, and since then I've seen it enough to give couriers at least an hour before I go searching for where they may have misdelivered my package. I think this is just something some individual couriers do because I rarely see it, but I have definitely seen it about a dozen to two dozen times in recent years.
I have NEVER seen Amazon do this kind of early tracking delivery, and in my experience they are by far the best carrier as compared to all the others. They do misdeliver at times, but for some reason it has always been consistently been to my neighbor on one side and not to the wrong street or some address nowhere near mine. A few years ago they delivered my packages five times in a row to that neighbor so I'm guessing their GPS had a bug.
What I don't get is why the devices from the carriers don't explicitly tell the carrier when they're misdelivering a package. The device should have everything it needs to warn the carrier that they've screwed up...so why are misdeliveries so common then? Does the software warn them and they just ignore it? I find the whole thing baffling.