While corys should not be kept in salted water on a regular basis, salt has its uses.
It does not burn them, but since they come from fresh water, once it is absorbed into their systems (through their skin) they cannot eliminate it. When kept in salted tanks, this leads to stress on their internal organs such as their kidneys and liver and could result in a shortened lifespan.
When I order fish from a seller online and they arrive in water that has a pH different from mine, I often add a little salt to their tank. It helps them adjust to their new home and within a week or two it's gradually removed from the water by frequent water changes.
I also use it when I have a cory that has a bacterial infection that does not respond to regular medication. In this case, I've successfully used strong salt baths where they are only kept in it for 10 to 20 minutes or so. I wouldn't recommend this to take the place of antibiotics, or the preparations they sell in the UK though. It's strictly something to try when all else has failed.
Big Mama is a wild caught bronze C. aeneus who arrived at the lfs with a batch that was so sick that some had no barbels or tails. Because it's so hard to get the wild caught ones around here, I took a chance and bought some of the better ones of the lot. After trying several courses of antibiotics, the infection was just getting worse. Eventually I gave up and tried using the salt baths with daily water changes and a little MelaFix in the water. It did the trick and after a week or so of doing this 4 to 6 times a day, they began healing and all of them recovered. I suspect they had very strong constitutions to begin with or they would not have made it.