Correct me if I'm off beam, Micca, but the definition of hard water is that the calcium or magnesium is dissolved in the water.
If you add an acid, which keeps the mineral in solution, then the water must still be defined as Hard, but would still be acidic.
You get rid of the hardness by making the mineral precipitate out of the water - by boiling "temporary" hardness (and forming lime scale in your kettle) or by converting soap into scum, thereby removing "permanent" hardness.
This would mean that it would be feasible to produce acidic "hard water". Likewise adding some sodium hydroxide to soft rainwater would make that alkaline, but not make it "hard".

SO - in a natural situation, because of the nature of the rocks and soil associated with Hard and Soft water, we would expect hard water to be alkaline and Soft water to be acidic.
BUT - in an artificial situation it would be possible for the reverse to be true.

Wonderful thing, science...
Quack!
GtD.