And if they shared actual results from such testing, they couldn't sell you anything ;)

Hydrolysis is just an inefficient process. Whether in or of a car. ICEs have been run off hydrogen alone. So just adding a little will displace some of the fuel the car uses. Any gains would just be lost when hydrolyzing water onboard. Then amount of hydrogen you can carry in tanks likely isn't worth the extra weight and lost space.

The only way to make hydrogen worthwhile on a car would be to reform it from the gas or diesel, and then putting it into a fuel cell might still be the only way to use it efficiently. Volvo has such a diesel fuel cell they plan on using as a generator in boats and trucks.
Volvo Plans Hydrogen Generators for Boats Kiss Diesel and Gas | BoatTEST.com