I reckon your analysis is right Paul.
The bottom line is that you can get today's internal combustion engines to run on hydrogen and you can get hydrogen from tap water through electrolysis. Therefore, in theory, you could get a car to run on tap water, in that the tap water would be the main fuel input but obviously the car would actually run on hydrogen.
.....I think :-/
I don't think electrolysis on-demand will be the solution, as you need to generate electricity to do that, and with a hydrogen engine the only viable source is likely to be an alternator. So you'll basically be using all the energy created by burning the hydrogen to create more hydrogen, and it still won't be enough due to energy losses. There needs to be an actual energy store, that will be used up and can be replenished -- this is what the boron provides in the previous example, with the energy ultimately coming from solar panels or similar. In that case the water is not used up per-se, it's just an enabler to release the energy from the boron (in the conversion to boron oxide) via hydrogen, with the water having a net zero energy output once it completes the cycle of being split and recombined.