I believe it's a myth that salt
can't be used in a freshwater tank with Corydoras.
Only some Catfish described as 'naked' are less tolerant of it but still shouldn't suffer any ill effects if the concentration of NaCl is correct to the volume of water.
As for the actual damage caused by salt to fish intolerant of it, I'm not entirely sure. At the least, I suppose, it would act as an irritant and induce stress and if that stress is sufficiently high, the immune system's ability to cope might be greatly reduced may leave them open to other infections, fungus, bacterial etc...
At worst, if a fish, for example a naked variety of Catfish (I think Loaches are classed as 'naked'), was exposed to NaCl, it could enter the blood stream. I don't believe there's then a mechanism for fish to eradicate that salt and therefore, perhaps, leading the fish to be poisoned.
I don't know any of that for sure, I am just using some common sense reasoning!
I'd actually love to know if any of that is true!!!