I think that's more perception than reality.
People who work around streams or in kitchens don't seem to have a constant urge to pee. I think the sound of running water does two things.
First, it reminds someone of peeing, and if they have to already it makes that urge conscious.
Second, running water masks the sound of pee hitting the pot and consequently makes it safe to pee without disclosing exactly what is happening. Social pressures somehow work to make people ashamed of natural processes sometimes, like sex.