Sure, so the way I understand it, a monad is a special type of arrow, so that's kille saying "You also live in France, so you'll have to be a bit more precise than Paris", no? I.e. both claims are equally true.
I think you have that the wrong way round.
Arrows also allow you to "multiplex on whatever is represented by a thing to choose a different thing" so you'll have to be more precise!