Why does Armory enforce a minimum transaction fee?
If the coins it is using have a lot of confirmations, the less likely a fee is going to be needed.

In the instance reported here, when the payment was sent using the Bitcoin.org client the funds had many confirmations and no fee was required. 

When a payment for that same amount was then created using Armory, the funds did not have many confirmations and thus the client insisted on there being a fee.

This is not a difference between Armory and the Bitcoin-Qt client.  This is a difference between sending coins which had lots of confirmations versus sending coins which had fewer confirmations.   The same thing would have happened regardless of which of the two clients was being used.