Actually salt will end up giving the Betta liver or kidney failures which is pretty much a death sentence.
I'm pretty sure I know where this came from since I also used to believe it although more for all of my fish than just Betta's.
I see Petco/Petsmart both dump a whole cup into all of their freshwater tanks each week (without dissolving it mind you....) and so people, without asking, think that doing that exact same thing help their fish too! In fact if you think about it, those stores pretty much have a high turn over rate so what they're doing is just preventing further infection to their fish and their tanks which is good...but also gives people the wrong idea when they don't ask what they're doing.
But since they have such a high turn over rate the fish actually won't be in the salt long. But of course just another thing to confuse people lol
So yes, while AQ salt (you can use Rock salt as long as it's pure NaCl, no additives) is great for treating infections, parasites and stuff like that, it should never be used as a therapeutic medication.