I too doubt very much that the USPS opens boxes just to see what's in them without good cause. I also doubt they deliberately damage them. If the boxes are splitting open from the handling, part of the problem may be with the way they are packaged. I've found in many cases, the cheaper the bullets, the less time and money spent by the seller to package them for shipment. When I get bullets from Graf's or Midway, they are generally double boxed with protective foam or airbags and arrive in good shape. When buying cheaper bulk bullets from some places they come in a single box with the only protection being the plastic bag they're thrown in and the order invoice. In the past, I've had the USPS open and reseal shipments like this to make sure there was no damage and to strengthen the poor job the shipper did on the package. There was always some kind of notice on the box along with a contact in case of damage/loss.
Also.......if you're so darn sure the post office is "sneekin' a peek" at your ammo, simple check the box next to UPS or FedEx next time you order. Most reputable sellers give you this option.