There are good acids and bad acids. ACV is a great one. But the problem is usually not too much acid, but rather too little. Then you take an antacid and the stomach occasionally produces a SURGE of acid (too much acid very quickly). This is what causes the burning symptom. Probably too why those suffering from not enough stomach acid think that their problem is too much acid.
Obviously the 'don't drink' rule is forgiven if it is for the tablespoon of distilled water you mix with the ACV...