"Natural annealing" and lead turning "powdery" strikes me as being fake news. Lead will oxidize, and given enough time it'll develop a white coating which is nothing more than oxidization, and is limited to the outside surface. Once a layer of it has formed, that's it - the main body underneath is still good old lead, the whole thing doesn't slowly turn to powder (at least for a millenium or two). That oxidizing needs air to make happen which negates the cores of jacketed bullets oxidizing out of sight inside the jackets.
Any shift in the hardness of the copper/gilding metal jackets on ancient bullets is so slight as to not matter a hill of diddly-squat for our purposes.
If the bullets in question were ever viable, accuracy and performance-wise, when new will be equally so now. I would be more concerned about concentricity and balance of said bullets if made a few generations ago effecting accuracy as compared to the technological marvels we enjoy today.
+1
Not the first time I’ve seen bits of misinformation on that site.
