The title more or less sums it up.
A rocket engine works pretty much by combining fuel and oxidizer, and expelling some propellant resulting in foward motion as described by Newton's third law of motion (colloquially, to each action there is an equal and opposite reaction).
Combining oxygen and hydrogen gives water in a highly energetic reaction: $$ 2\text{H}_{2} + \text{O}_{2} \rightarrow \text{H}_2\text{O} + \text{energy} $$
The water (vapor) has to go somewhere, and as such is ideal to throw out the back of the rocket.
Consequently, is it correct to say that a LH2/LOX rocket engine uses water as propellant? If not, then where is the flaw in my reasoning?
