I can understand that logic, though from my understanding its the salinity, not the hardness of the water, that allows skimmers to work in SW
but not in FW
What are you using for an alk
supplement? Maybe the skimmer is skimming the supplement out? I've heard lots of rumors about skimmers removing trace elements and such. We know slime coat enhancers and even some dechlors will make a skimmer go crazy.
However I've never seen a skimmer expert sit down and commit an answer of yes or no about whether a skimmer can remove that stuff from the water column or not. Maybe we need a chemist/engineer