Mollies can be healthy in freshwater without "salt," but they must have minerals. The two are frequently confused/misunderstood.
Mollies are freshwater fish. While it is true that the wild fish sometimes occur in brackish waters such as coastal estuaries, they also inhabit completely fresh water. The wild fish is almost never seen in the hobby, and the generations of commercially-raised fish such as those farmed in the Far East have almost certainly never had salt in the water.
Hard minerals however are absolutely essential. The calcium and magnesium levels in the water are crucial to the health and physiology of this fish, even more than with other livebearers. The GH of the water must be moderately hard or harder, with a basic pH [meaning, a pH above 7 and preferably in the high 7's plus]. If your source water is on the soft side, it is fairly easy to raise the GH with calcareous substances like aragonite/crushed coral sand, either as a substrate or in the filter, but keep in mind that this should be done in a tank devoted to the mollies (and/or other livebearers), as soft water fish are the exact opposite and will weaken with increasing hardness.
Plants are a good decor with mollies, as they naturally spend their time grazing leaves for algae. Vallisneria does especially well in molly tanks since this plant does well in similar water.
Byron.