Dishwasher guide: salt will harm the stainless steel lining. What about salt water in stainless steel pots?

The manual for my dishwasher says to refill salt just before running a wash cycle, because if any grains of salt spill onto the stainless steel interior it will corrode. If it runs right away, no issue because the salt is quickly dissolved, diluted, and flushed.

So then I realized when I cook pasta I heavily salt the water (following the advice that pasta water should taste as salty as the ocean). But what happens when I leave that highly salty brine in a pot, sometimes for a couple days to reuse it? Does that risk corroding the pots?