Actually, it can be a sound business move.
Two words come to mind: vertical integration.
If they take over more components within the chain that makes their business possible, that can be a key cost reduction and allow them to compete even more fully.
The (likely?) mistake would be if they were to expand outside of their core business. In this particular example, if they were going to try and use this delivery mechanism for "more than just Amazon packages" and offer shipping options to competitors, they may expose themselves to greater chance of failure because, frankly, their core competency isn't "shipping."
Think of it this way: since FedEx/UPS are looking to make a profit, they must charge an amount that has parts X (actual costs for people, vehicles, equipment, etc. to deliver a package) plus Y (the amount to be profitable).
If the shipping is such a core part of Amazon's business (which it is), then eliminating the "Y" portion of the overall shipping costs in favor of absorbing the overhead of managing the X may boost their revenue significantly.
Given the volume they ship and how core that is to them being successful? I think it makes perfect sense for Amazon to consider eliminating the middle man and seek to deliver packages directly to their customers. The REAL question is: can they actually do it? Lots and lots and lots of logistics, planning, new systems, new solutions... plenty of opportunity to screw it up. But, IF they can manage it, then it can be a serious game-changer in Amazon's favor.