I think it depends on what they were kept in when you got them.
No, that's a myth.
Here's the deal:
In the wild Mollies mostly live in freshwater. Usually not far from the sea, so very much the coastline of North America through to Brazil, but in freshwater nonetheless. They do live in brackish water in some parts of their range though, and occasionally get exposed to fully marine salinities, for example in mangroves.
Aquarium Mollies are not a true species. They are ALL hybrids of one sort or another. Like their ancestors, they can do just fine in freshwater. But generations of aquarists have noticed that Mollies are always easier to keep when a little salt is added. This doesn't mean you can't keep them in freshwater, but rather the probability of disease becomes less when salt is added.
The reasons for this are unclear. There are three possible explanations. The first is that some Mollies have more "brackish water Molly" genes in them than others. I used to believe this, but I'm very skeptical now. The second is that sodium chloride reduces the toxicity of nitrite and nitrate, both of which cause problems for Mollies. Contrast the fact Mollies are sensitive to water quality in freshwater tanks to the fact they were used to cycle marine aquaria where they could be virtually guaranteed to get through any nitrite spike you might have to deal with! Finally, there's the increased carbonate hardness provided by marine salt mix. This buffers the pH, preventing the inevitable pH drops you get between water changes. Again, Mollies seem to be acutely sensitive to low pH, perhaps more so than other livebearers such as Guppies or Platies.
The use of marine aquarium salt mix provides a two-fold benefit: reduces nitrite and nitrate toxicity, and then buffers the pH and reduces problems with osmoregulation. Plain aquarium salt only provides the first benefit, which is why I don't see any point to using it. If you're going to add salt at a meaningful concentration, you may as well use proper marine aquarium salt mix. There are plenty of compatible fish that tolerate SG 1.002, including such things as Australian rainbowfish, horseface loaches, brown hoplo catfish, common plecs and quite a few cichlids. Lots of plants thrive at this salinity too.
Cheers, Neale