Doing a little out of the box thinking here I have to wounder.
These birds are migratory birds so if they told the truth or the hole story there is no telling where they got the led form but my guess would be a third would country or china / japan somthing like that remeber birds can not read warning signs so they may visit some real bad waters closed to the general public..

Here is some food for thought if you think about it our world is allways shaking/moving very small earth quake so if you take a piece of led and put it in some soft sedment or sand and water what would happen it would go futher down in the mud sand or what ever in short it would just keep sinking until it hit the hard pan or lime stone sorry but what there feeding us is BS at its finest and just another way the anti hunter is trying to shut us out.
Another thing to think about is when they lower the lakes how many people go around and pick up the led ? how many baits and sinkers have you picked up?. I know not all lakes are droped but even the ones that are not some times go thrugh a low level now and then from the lack of rain.

There is too many varables to point the finger at one thing. If you never had any contact with led your hole life and got tested for led you would show pos. why It's in the water you drink...