Doing no research, I think Dala is right about turkeys not flying. I spooked one while running in the country Saturday, and it just made a lot of noise and jumped and flapped about. There are also wild but urban turkeys in town. I've never seen them fly, just jump and flap.
Unrelated to turkeys but related to animals and my run, I also garnered some interest from cows. I waved and said hi. Cows seem lovely. I also got barked at by a hound with a really deep voice.