That paper doesn’t say anything about a relationship between routine variation in fluid intake and sodium concentration, or did I miss it?

It’s undisputed that in pathological states, hyper- or hyponatremia can occur. And the formula in the paper you linked gives a solution to calculating the free water deficit (for example). But it’s not the same as knowing that modest variation in fluid intake can be seen in sodium concentration (because it’s homeostatically regulated).