Actually, Fedex does ship live animals. According to the policies on their website,
www.fedex.com, they will ship animals under the following conditions;
(this is copied and pasted directly from their web site)
FedEx Express Terms and Conditions
Live Animals
FedEx does not accept live animal shipments as part of its regularly scheduled service. Live animals will be accepted when the shipment is coordinated and approved by the FedEx Live Animal Desk. Acceptable shipments include, but are not limited to, zoo animals (to and from zoo locations only) and horses (from gateway to gateway locations only). Household pets, such as domestic cats and dogs, are not accepted. For more information, please contact the FedEx Live Animal Desk at 800.405.9052.
Tegan, you may have had a problem because you were trying to use the regular service to ship (although you did state that you called the Live Animal Desk). I'm guessing that since the wording of the Terms and Conditions is a bit vague in some respects, that it may be up to the discretion of the specific person you deal with at the time. (of course, they will never admit that if you ask.)
My advice would be to find a different method for shipping. (hint-the regular post office is nothin but trouble as well)
Better luck next time.