Funny you should ask.
Our IT guys just screwed up both UPS & Fedex's systems here at work just last week. I'm a programmer at a distribution company, and had a front row seat to the mess.
We had a power surge that fried two of our shipping stations, and the last backup was about a week old. Since all the stations are identical, they cloned the hard drive from one station and put the image onto the two replacement stations, thereby getting them up and running quickly.
The imaged system and the replacements then started generating identical tracking numbers. While the packages arrived correctly (the address is encoded into the barcode), the tracking information was garbage on the both companies websites. It would show packages jumping from California to Georgia in a matter of minutes for instance. Packages were delivered multiple times, etc. No major harm was done, but customer's who were attempting to track their packages were very confused.
Not sure what you can gleam from this, but at the very least it's obvious that neither company treats the tracking number as unique, and they don't use them for anything of importance internally.