when ever I encounter a hunter that is clamming the bird, I give him the BIRD

We always use rock, paper, scissors...

I'd just work on getting enough birds that everyone limits (even if I was the one to shoot them all (har, har, har))

While pheasant hunting, where the birds are divided up at of the day, I always yell good shot when someone shoots at the same time. It's just a more enjoyable walk with an empty vest.

I just hunt with my dad mostly, and at 70yo he can still out shoot me, so I just assume it's his!

testify brother testify!

Never make a bird hunt a contest unless you agree upon it ahead of time... i.e. "last one to limit buys dinner"
Most guys I hunt with know who killed the bird and you'll never hear one of them claim a bird.

In the example you give, the first guy to hit it should thank whoever finished it off and feel fortunate that someone made up for his poor shooting that would have otherwise resulted in a lost bird!