I work for FedEx Kinko's, so hopefully I can give you a little insight.
1) We are not allowed to package or ship packages out of our location that contain any type of live animal or fish. This does not mean you can't send fish via FedEx, just that FedEx Kinko's locations are not allowed. I believe you can ship them through a World Service Center.
2) If you do ship via FedEx, or any other carrier (UPS, USPS, DHL) keep in mind that the box has a long way to go. The box starts at the dropoff spot. It is then transported to a sorting facility. In the sorting facility the box will take about a 5 foot drop (make sure you package properly). From here it will go on another truck or carrier and then go to either a plan, or another truck for ground transport. Once it reaches the airport or next stop, it then goes through another sort and drop, and then gets put on the local couriers truck for delivery.
3) You receive your package and hopefully are happy.
In order to file a claim with FedEx, typically the packaging will be inspected to make sure it was packaged properly. These people are pros in packaging and know what a box can or cant handle, how effective the packaging material was etc. If you're fish just dies, no carrier will reimburse you for it. That is just out of their control. A lot of the dead fish stories I here tend to involve the cold weather and no/only one heat pack.
For the most part shipping fish is pretty safe.... millions of fish are shipped daily to LFS, etc. I think the dead fishes you here about are more the exception rather than the norm. My advice is too not skimp on the packaging. I find it nice when someone ships me a fish in a nice new box with thick styrofoam on all sides (like a cooler). Packaging really is the key, I cant stress that enough. My Flowerhorn came that way, and it took 3 days to get to me and he was in perfect shape.
Just my .02.