It doesn't, obviously, since it's not possible to prove a negative. Much like there's nothing that proves that you won't begin to be able to fly if you stand on one leg long enough.
If what you've been shown so far is insufficient evidence for you, then I'm afraid you're on your own. I don't need to play the "how about this" moving goalpost game.
Low quantities of lead have exactly the long term low-dose exposure effects you describe. They have been identified.