It is absolutely electrolysis. You can try it yourself with a battery and dish of water.
It's absolutely not.
I already tried it myself with a 3MW generator and a giant tank of saltwater.
The fun part: it does both!
I see your point, though we barely ever had to top the tank up with water or salt. The amount of gas created was minimal, at least with our setup - admittedly not as fancy as a battery and a dish of water ;)