If it's any consolation... whenever I wire residential which is rare, I keep all lighting on 15a circuits seperate from everything else, and now I wire all receptacle circuits on #12 awg. 20 amp wire, even if it lands on a 15a breaker.
I'm still a proponent that having more 15a circuits is better than having less
A *better* test would be if you could light a 300W bulb using the water pipe for a return path. But what happens if there's a leak to ground in the dryer, and it's not enough to blow a fuse (breaker, whatever.) That's a good way to electrocute a plumber someday who disconnects the pipe somewhere in the middle.
You are safer using the dryer equipment ground as a neutral because it's a big wire and the unbalanced load for a dryer is very small.
In other words leave it alone, or run a real ground wire back to the panel (or the grounding electrode conductor, or the electric meter enclosure, or the copper pipe on street side of the water meter, or a ground clamp on the metal service raceway.) The ground wire is supposed to be run with circuit conductors, but doesn't have to be for old work if doing so is totally impractical.
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