Coca-colas have a pH of 2.4 to 3 [1]. Stomach acid's pH is 1.5 to 3.5 [2]. So coca-cola has acidity that is very close to that of stomach acid. Water's pH is around 7. I am no doctor, but wouldn't that suggest that drinking water will unbalance stomach's acidity worse than coca-cola will?
Yes, but you are still adding a significant amount of acid to the stomach, way more than is supposed to be there. If your body can't neutralize the extra acid fast enough (to pass to the S. Intestine for adsorption) then you are either going to have a stomach ache, acid reflux or you may vomit. That's why people take chalky antacids to deal with an overly acidic stomach - your body naturally produces bicarbonate to do that, Tums provides a larger dose.
No, it just means our body knows very well how to regulate less acidic stuff coming in, all day, everyday. One can expect in that case that digestive system is not perfectly balanced around ph of stomach in both directions, but rather overequipped for the most common case, and underequipped for the opposite.
[1] https://www.ada.org/en/~/media/ADA/Public%20Programs/Files/J...
[2] https://medlineplus.gov/ency/article/003883.htm