I am not sure about the whole "working out requires eating salt tabs", when I was doing triathlons a lot of people took them and it was amazing seeing all the salt that ended up on their clothing due to sweat/evaporation. I've always thought that if you really needed the electrolytes your body wouldn't immediately try to get rid of them via sweat.
Again of course this is n=1, I think maybe my n=1 is different because I am used to an extremely low sodium diet, but goes to show that when it comes to diet it's all a big YMMV...