From the Don't Shoot the Messenger Department
If I read that FWC web site correctly, when they say "mallard" they mean all mallard-derived domestic breeds. And their stated concern is that the domestics will produce viable offspring with wild populations of spotted ducks.
The pet permit, if...
Oh, mercy, look what I turned up.
http://myfwc.com/wildlifehabitats/managed/waterfowl/mallard-possession-rule/
Here is the free personal pet permit reference
1) No-cost Personal Pet Permit for Class III Wildlife (includes mallards).
(Per 68A-6.002)