I'm guessing that **** (my asterisks) is one of many things that heating the pot far above boiling point would definitively put right. With lead it is likely to produce that fateful conversion to oxide. Also if you eat a bad oyster raw and come out on your feet, the offending substance and its bacteria are eliminated from your system in a day or two. Lead, like most heavy metal poisons, is lasting and cumulative.
I'm not sure how much difference the acidity of Roman wine made. Nitrocellulose used to be made with hot and concentrated nitric and sulphuric acid in lead vats, which weren't much affected. They also had lead water pipes, the ones that could afford it, and that is likely to be several yards per wine-jug, and the jugs and cups were short-term containers.