The urban legend usually just leaves the electrolysis part blurry. They vaguely call it a machine to process or prepare the water, and completely ignore the electricity going in. I.e. hydrogen cars, being "suppressed" by the government.

The urban legend goes back a long time. I first encountered someone telling specifics around 15 years ago, but the vague concept is much older. It's similar to the legend that there's a specially tuned carburator (yeah, that old) that would give you 100mpg, but it was killed by oil companies.