Extreme salt reduction leads to hyponatremia, which causes heart, and kidney failure. Most everyone with a sensitivity to salt probably just has a deficiency in magnesium or poor glucose metabolism.
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The (Political) Science of Salt:
The opinion of some scientists working in the area, and based on data that's as good as anyone's got, would seem to be that even hypertensives would see little benefit from sodium reduction.
I think this issue may have been something of a stalking horse for the saturated fat issue for Taubes (although when he first began looking into that he had taken the ideology that's offered to the public about it hook, line, and sinker).
What we would seem to have -- as with saturated fat -- is people knowingly going far beyond what was warranted by the data on the basis of hunches, working on the basis that if we wait till we do know it'll be too late for people ... and not understanding that if the hunches are wrong then the leap of faith gets us precisely nowhere. Then you get a much larger number of other, less well-informed, people with weaker understanding who take an under-determined case as fact without even knowing that there's any doubt.