Contractors who install FedEx for their customers please note:

In order to get a production API key, you require a Shipping Account to be associated with your developer account.
The creation of a shipping account must be done by an employee (not a contractor) of the firm that is doing the shipping.
To make this a bit more clear, I updated the documentation to put the shipping account creation up front. Get your client to do this, then you can do the rest.