Since this topic has happened in the "New to the Hobby" section, it might be helpful if one of the experienced members could review the reason why, for beginners to hear, in the 1950's 1960's, when the principles of ammonia and nitrite problems were not widely understood, negatives of heavy metals and organics buildups were not widely understood, and water changes were frowned upon, the action of salt either did or was thought to lessen the negative effects of lack of water changes.
I've got some books that cover it pretty well, so here's the rough rundown - as usual when people are playing scientist, there's probably a dozen variations (the books disagree on a few things, as well). Having never actually done anything like it, I can only give a rough review of the books and mix in some fish-store standard advice I was handed when I bought my tank. If anybody actually did this, or at least kept fish when it was done, I'd love to hear their take on it.
The biggest thing comes down to a poor understanding of the cycle process. All the right observations were there, but they were being connected wrong.
A tank was set up, fish were added, fish stressed and often died (the new tank syndrome many still deal with to this day). However, after a month or so of this, fish would survive. Today, we have a good understanding of the cycle, where bacteria form, and so forth. However, in the past, it was a common misconception that the *water* cycled, not the filter, which is why to this day, even with the better understanding, you often hear on this forum not to change too much water at a time, because you lose bacteria.
So, the noise was about "old water." Water that had fish in it for a month didn't kill fish, water that hasn't had fish in it did. So water changes were avoided, and water quality went south. High nitrates, pH crash, the whole nine yards (One of the old books my grandfather gave me even mentions the pH crash as the measure of a "mature" tank, the other correctly recognizes this as a bad thing and has a list of products and DIY solutions to prevent it*). Fish that were in the system through this often survived, but new fish introduced into it would often die - this is what we call old tank syndrome today. One book puts this up to nebulous "weakness" in the system, the other repeatedly calls it "captivity stress," as if to say it was an unavoidable byproduct of confining fish in glass. Water changes at this point actually can actually shock the fish to death if water quality improves too quickly, which reinforces the concept that the old water was better than the new water.
Salt happens to reduce the toxicity of nitrates (and nitrites during a fish-in cycle). So, in these methods, salt did decrease the considerable (and sometimes fatal) stress that the method put on fish. Old tank without salt: badly stressed, dying fish. Old tank with salt: much less stressed fish. One of the two books notes that "salt doesn't entirely eliminate captivity stress," what we know now, it was just trading a greater stress for a lesser stress.
Another thing I note, both books suggest that there's no way to run a tank for more than 1-2 years without entirely tearing it down and cleaning it out. My take there (just a guess, maybe somebody has better info here), is that ultimately, all the above is just a stall. The system simply isn't sustainable like that, eventually the water quality will decay to the point that salt can't help anymore.
* - the DIY solutions are the same that get mentioned today in regards to pH during a fishless cycle. If you think about it, a fishless cycle is a lot like leaving a tank running too long without water changes.
Edit: As for the books, they aren't exactly high literature - one was a local fish club publication given to new members, the other seems to be a real publication, but missing the cover I don't know who wrote it. From something Rabbut said, it sounds like better methods existed even then, and I do have a TFH publication from the late 70's which gives passable advise on water changes.