Basically they're saying that shooting animals leaves small amounts of lead in the meat. Rare birds (eg condors, eagles, ravens) eat the meat and offal, and get lead poisoning. Maybe humans could get sick too.
This conference is all about lead residues from shooting deer with rifles. But the argument holds true for shooting rabbits, foxes, etc too, since they may end up as food for corvids, raptors and others. And you can bet it won't be long before lead shot cartridges are in the spotlight too.
state health officials recently ordered food banks to discard donated venison
The American Bird Conservancy has put out this press release showing x-rays of venison meat containing lead fragments, and claiming that "new studies suggest that humans who eat game shot with lead ammunition may be at risk". It goes on to make wild guesses at what the effects might be: "Recently published research suggests that even very low levels of lead exposure in children can cause learning disabilities, and in adults may increase risk of Alzheimer’s disease and death from stroke or heart attack. Lead is also associated with impaired visual and motor function, growth abnormality, neurological and organ damage, hearing loss, hypertension and reproductive complications."
Deliberately emotive stuff, and sufficiently vague to give lead a bad name without actually proving anything. It's the old trick of flinging mud at the wall, so some sticks.
Is lead really a danger to wildlife and humans? My view is that in the end the truth won't matter. If people believe it's a danger, that will be enough. We won't win the argument by shouting "prove it" – especially if it turns out they can!