These accounts are much older, usually from way before 1920, while there were still tribes that were eating their traditional foods.

Another factor that comes into play is apparently that the kidneys become much more efficient at retaining sodium. You don't excrete as much, if you're not taking in very much.

And...why should sweat be salty? Presumably, for people that don't add any salt to their food, I'm guessing that their sweat would be less salty. Maybe not even salty at all.