Saturation Index clarification
Why don't you think calcite is forming in-situ? The saturation index does not guarantee that calcite has precipitated (or dissolved) but there are a number of reasons to think it has. First, calcite does not have a large kinetic barrier to precipitation. The kinetics are fairly rapid. Rapid is a relative term but the formation of calcite in caliche and speleothems indicates that it does not take much for it to precipitate. Secondly, are you suggesting that it is merely coincidental that the SI indicates saturation? Do you have a number of water samples from different locations that are all in equilibrium with calcite? How would that occur without reacting to form or dissolve calcite? What else could be buffering the pH to the value at equilibrium between your solution and calcite?

Have you looked at the gypsum SI? Does it remain undersaturated? If so you would expect it to be dissolving which would move calcite towards supersaturation.

One possibility is that you in equilibrium with both gypsum and calcite. In that case, they will fix the ion concentrations in solution and pH so you get no further precipitation (assuming the system is closed to carbon dioxide).