[LucianOfSamasota]

Don’t birds eat small rocks for their gizzards?

How soluble is metallic lead?

[TigersEye]

I couldn't find much information on that but here is a study on the incidence of lead shot ingestion by waterfowl. It's a very detailed study (which is good but tedious to read) and from skimming it what I see is that the percentage of birds who ingest any shot, lead or steel, is very low. The percentage that ingest enough to get sick and die is even lower. It says on average a piece of shot only stays in their gizzard about 20 days.

A Review of the Problem of Lead Poisoning in Waterfowl

It doesn't say anything about proving that any waterfowl actually get sick or die from lead poisoning which would require tox screens of blood or tissue samples I am guessing. My take from that study is that it's a non-issue.