Carbonates don't really have much flavor, though. It takes a LOT of chalk for me to be able to taste it, even in water.
Granted, the flavor could be something else in the water. But it's certainly not sulfate, since I've never tasted it in an IPA. Perhaps there is a level of chloride between 'enhancing malt sweetness' and 'nasty nasty saltiness' at which it produces flinty flavors.