We have a FedEx 9-digit account number in the form of "0171#####". However, this package takes "account number" literally (sensibly so) and types all the $accountNumber's to int. This, in turn, causes our account numbers to be sent through as 8-digit numbers in the form of 171#####, which then causes all our rate requests (and, presumably, any other account-number-based request) to fail.
To solve this, $accountNumber should be treated as a string.