I work day in day out with a carrier company, managing massive thousand pound orders that 'go missing' and we get some right idiots.
Majority of them turn up sooner or later, those that don't get claimed back on the carrier. Once they leave our premises the goods are the carriers responsibilty and therefore hold value with them, rather than ourselves. The carrier should have some insurance policy to cover you, whatever the items are, to protect from lost or damaged stuff but i'm sure there is small print etc which would probably mean it proved difficult to get any sort of compensation.
Chances are the other boxes have become detached from the top, labelled box and are sat in a sorting depot somewhere, with no address on...and sadly that is probably where they will stay (unless a returns address or similar was added to the package) Company's such as UPS handles thousands of parcels a day. Those with no labels will just get thrown into a holding bay and unless distiguished from other boxes, just won't move anywhere.
Best thing to do is ask for a POD (proof of deliv.) and UPS should be able to supply, in hardform, a copy of the recipients signature/delivery time/address etc as proof he signed for the goods. You ONLY sign for goods once checked and happy with, if he chose not to, or didn't have the common sense then he is at fault. It could well be those 3 other boxes were sat on the lorry and had become detached during transit. In which case a simple word with the driver may have sorted this whole mess out their and then, at the time of delivery.
I can't see how you are at fault. If he'd done everything in his power to trace the wheels i'd understand, yet he's signed for 1 box, knowing full well he is to recieve 4 wheels, has let the driver leave again and then complained about it. If I were you i'd keep your money in your pocket
Ta
Mish
