Fortunately there is no forensic evidence that I have ever seen which links higher lead levels and eating game shot with bullets containing lead. You would think there would be a few thousand hunters with high levels of lead poisoning after 150 years of shooting critters with lead bullets. Yet I have never heard of the first one. I'll keep slinging Bergers, Lapuas, and Hornadys at stuff and my family keeps eating game and feeling great. Its all good but I think the non lead craze is perhaps a little overblown.
Fact Sheet on Lead in Venison
Second paragraph pretty much sums it up. Little or no evidence of danger from lead in venison.
Lead Ammunition Is Not a Health Threat to Humans | Hunt For Truth
And more contrary news. Lead poisoning from bullets = fake news.
I do see your point. However the difference between human and wildlife lead poisoning/consumption could be linked to the fact that we discard the blood shot tissue and guts as we don't see it as desirable to eat; this discarded product would likely contain the majority of lead fragments.