Lead poisoning is not caused by ingesting a chunk of metalic lead. That lead passes right through you. You get lead poisoning from longterm exposure to lead in the air, water, and objects you are constantly touching. I suppose it may be different for birds since they have a gizzard. maybe chunks of lead are ground up in a gizzard. But why is it birds never had a problem going extinct until now? Obviously there is something other than lead bullets causing these birds to die off.
I'd like to see the results of autopsies with special attention to gizzards. Metallic lead is fairly unreactive.