If you read it, note that the authors usually refer to salt in grams per day. In the U.S., we typically talk about dietary salt in terms of its sodium content, also in grams per day. Table salt, remember, is NaCl (sodium chloride).
The theory is that high salt intake raises blood pressure, which leads to premature death or disability from heart attacks, strokes, atherosclerosis, and aneurysms. Cut your salt consumption, and blood pressure comes down to a safer level.
You can find studies that don’t support the theory.
From the BMI article:
In the United States, it is recommended that sodium intake should be reduced to less than 2.3 g/day (equivalent to about 6 g/day salt) for most adults, with a further reduction to 1.5 g/day (4 g/d salt) for about half the population, including African Americans, all adults aged 51 and older, and individuals with hypertension, diabetes, or chronic kidney disease.
From the evidence above, it is clear that the recommendations to reduce salt from the current levels of about 9-12 g/day to 5-6 g/day will have a significant effect on blood pressure but are not ideal. A further reduction to 3 g/day will have a much greater effect on blood pressure, and we consider that this should become the long term target for population salt intake.
A pure paleo diet is a low-sodium diet.