Uh, I guess I should have paid closer attention to the original post "from the BURNER to the top". I was in the mindset the the top was energized and the measurement was being taken from it to perhaps the sink plumbing. That makes a big difference.
No doubt, the burner(s) has failed. Most appliances only switch one leg of the 208/240 feeding them, so a fault would certainly be capable of energizing the coil itself even if turned off.
Another plug for smooth top ranges, I suppose.
