Well, sorta.  The lye doesn't react *that* quickly with your skin.  So getting it on your skin isn't going to have it dig in that fast.  And, btw, adding more WATER to it, if you have lye on your skin is a *major* no-no unless it's water filled with soap.  Otherwise, you want to use liquid soap first on yourself as fast as possible, and then use the water.  Oddly enough, the liquid soap, most of them, neutralize it quite well.

But the nasty burns from the scalding water?  Yeah you got it 100% correct.