I'm going to respectfully disagree with your statement. The salt content of our sweat can, according to some training articles, be up to 2000 mg per liter. That's nearly a teaspoon of salt. I'm willing to wager most of those former marathoners croaked due to hyponatremia, which is an actual thing, especially now that so many authorities recommend low salt intake. People stop sweating, and the myriad electrolyte-regulated processes, including but not limited to heart function, are disrupted.
I was particularly intrigued by one article that claimed one can measure one's own sodium loss via sweat, and that there is a great individual variation in this. The link can be found on a site called TrainingPeaks, if anyone is interested. I'm not a poster of links, but today's google is remarkably effective at finding items.
I've taken to leaving a bowl of water by the door for my 17 year old cat, who seems to find the AC too cold for his liking. 😉