The element probably is double insulated, which is why you don't get shocked when it's hooked up properly, when it's not hooked up properly the tip is directly connected to hot line, the element doesn't care which side is live so the iron will work just fine either way, you'll just fry yourself and apply 120V ac to anything the tip touches. I was a bit mistaken on the double insulation I mentioned above, it doesn't mean squat if the polarity is reversed.
I'm guessing you have a switch on the iron? It's quiet common to only switch the live wire on AC connected devices, since your polarity was reversed even with the Iron off the tip still had 120V AC applied to it. The switch was disabling the neutral line which stops the iron from working, but a human touching the case grounds it relatively well.