This theory is predominantly based on plenty of case studies, observational data, anecdotes and expert opinion (what scientists call “level 4 and level 5 evidence”).
One example is a classic study on salt depletion that was carried out by a pioneering doctor—R.A McCance—in the 1930s. Essentially what McCance and his co-workers did was subject themselves to an incredibly low salt diet. Along with their salt-free food, the subjects drank plenty of water and took hot baths to increase sweat output and accelerate salt loss. They found that when salt depletion started to kick in it quickly led to:
“… aberrations of flavor, cramps, weakness, lassitude, and severe cardio-respiratory distress on exertion.”
Interestingly, as soon as the test subjects reintroduced salt into their systems (eating bacon and drinking the fat from the pan I might add) their recovery from these symptoms—including the absence of further cramping—was dramatic, with effects being felt within 15 minutes of ingestion of the salty meal.
This experience in particular, cramps disappearing soon after salt ingestion, is completely consistent with my own experiences in very long and hot triathlons when I had become salt depleted due to heavy sweating. As such it definitely struck a chord with me when I first read it.