I have a SWC so I know I need to have salt in my pool, but I am a little confused as to why people think that soft-water = salt-water.

I was always under the impression that water softeners used salt in a brine solution that backwashed the resin or media that is used to take those hard minerals out of the water to make it soft. Salt is not added to the water to make it soft, even though I have read where softeners have warnings to people that are on a low sodium diet, and I assume thats because a small amount of salt is left in the softener media after backwashing it which can get into the soft water coming out of the softener.