Absolutely.
I think partially the definition of 'monk weapons' is based on narrative, and partially is a balance factor, mostly to exclude weapons that have large base damage, but for that it might have been enough to avoid martial weapons, should the Monk find a way to become proficient. However, bows and crossbows might have been purposefully excluded to make sure the Monk won't be a great ranged combatant (but IMHO she can still be, it's just that she can't use the Martial Arts benefits with projectile weapons).
Only the definition of 'monk weapons'
See that 'monk weapons' and 'weapons which monks are proficient with' are two different things. The latter include some weapons which are not 'monk weapons'. By 'monk weapons' we mean weapons that can be used to gain the benefits from the Martial Arts feature of the Monk, and that's where you'll find the sentence that says that they have to be simple + melee (but not heavy or two-handed).