Water can have alkalinity and an acid pH. This is due to the bicarbonate ion, which is very weakly acidic. It is important not to confuse alkalinity with 'pH above 7'.
The breakdown of foods as you mention is important to the acid alkali balance. Fats, carbohydrates and protein are broken down to carbon dioxide(sightly acidic) and urea (slightly basic). The quantities outweigh the amounts of free carbon dioxide found in natural water. I am not talking about carbonated water (soda).