I don't think it has so much to do with availability of water. There's PLENTY of water in ND on a wet year, and the ducks still dry feed.
I think it may have more to do with where they are in their yearly biological cycles. Ducks are made to live in wetlands, bottom line. Can they walk on land, yes, but on dry ground they are cumbersome and awkward. They have lived this way for thousands of years prior to commercialized agriculture taking over the landscape of North America. However, in the fall as they are beginning their migration, they are willing to change their natural habits of feeding in wetlands in exchange for the high carbohydrate levels present in cereal crops. They realize that their bodies need large fat reserves and are willing to do what it takes to get them (ie: dry feeding).
As they come further south, ducks aren't as desperate for the carbs and are switching over to more protein based diets to prepare for pairing, breeding, and nesting. Sure they will eat corn if it's in a convenient wet spot or flooded field, but they aren't as willing to leave their natural habitats in search of calories as they were a couple months earlier. This explains why mallards in NY and PA will pile into corn fields, but when those same birds reach MD, VA, and NC, they are rarely found in dry fields. I have seen mallards feeding a dry corn field in Eastern NC once, but it was really cold, Lake Mattamuskeet was locked up with ice, and all the birds were getting ready to move out of the area within the next day.
Geese on the other hand nest on the tundra, often times long distances from water. They are large enough to keep back most aerial predators and are decent at navigating dry land on foot. Thus, they feed on dry land more readily than ducks.