If the water pump is leaking you should be able to find water/coolant making it's way out from the timing cover. If you never need to add and you don't find water (take the timing cover inspection cover off) I'd wonder how they diagnosed it.
Most hondas (if not all?) have interference design engines. if the T-belt breaks a piston will slam into a valve causing major engine damage. Timing belts on Hondas should be replaced every 60 or 90k miles. When changing the belt it's commonn practice to also change the pump cause "you're already there" in terms of labor. The opposite is also true since the belt must come off to change the pump.
If they can convince you (or convince yourself) that it is leaking change the belt along with the pump.
I just saw a 1988 560SL with 40K miles and the pump bearing is leaking.
1982 300D Turbo