It does not seem to apply to throwing. It’s been tested with shurikens and throwing boulders on red.

If you're talking about what I think you're talking about, I suspect it's just a client/server sync issue and not a bug because it still happens on Live, as well. It's not limited to bow, either. When you attack with bow it doesn't automatically switch to showing bow as the visible weapon, nor send an update packet from the server to other clients to reflect a weapon change. If you equip/unequip the bow then it will update for everyone because it forces the update packet.

You can easily test this on any character already by just re-equipping your range item and then autoattacking something in melee. You'll be autoattacking while holding your range item. Same concept in reverse.

From what I’ve tested by quizzing other players for what they see… Equipping the bow doesn’t even display it to other players.