[amluto]

The placebo was dilute lactic acid of similar pH. So one might imagine that the acidity didn’t cause the effect and try neutralizing the vinegar. Add, for example, calcium carbonate (cheap and safe) to convert most of the acetic acid to calcium acetate, leaving a neutral solution with extra calcium. Whatever magic other compounds in apple cider vinegar are beneficial seem likely to survive that process intact. The net result would be similar to drinking the vinegar and eating an antacid, minus the tooth damage.