I'm a lifelong resident from that area. The Chesapeake Bay is a major destination for migrating birds. This link claims that the Bay currently receives a million birds each fall and winter. https://www.fws.gov/chesapeakebay/migbird.html

During the 19th century, Hampton Roads was a popular vacation site for duck hunting clubs. I've heard it was easy pickings until excessive hunting took its toll around 1920 or '30. For confirmation of that, check out the website for nearby Virginia Beach's Atlantic Waterfowl Museum.

It therefore seems plausible to me that Smith was surrounded by masses of migrating geese and ducks, and that those birds saved them from starvation.