Oh man, you just touched on my biggest animal fear! I have never been a bird person. In fact, I didn't even want chickens but when faced with my little peepers going to the pound, I brought them home instead. Now I love my girls (not too keen on my spawn-of-satan rooster though).
On a daily basis, I will have tons of doves, sparrows, ravens, quail, or startlings right outside my sliding glass door. In the last three years I have almost had three sparrows and a falcon fly into me (missed by mere inches), a hawk nearly drop a dead pigeon type bird on my head, and a raven fling a dead rabbit at me. Birds are not my friend!
But that is a good point. The birds, dogs, or any other animal that eats from the contaminated, should also become a threat you'd think.