Okay so this came up a bit over a year ago, was addressed and has come up again, and it will be addressed again.
Mages are secretive and paranoid by standard just because someone does not offer you the order it does mean they are an instant guardian, it does not eliminate any possibility over any other possibility because their not telling you can just as easily be a personality trait, or done out of safety.
In meeting in the Tower Joyeuse can only safely assume Witch is not an arrow because Witch has said that and is not in the arrow meeting. It is still just as possible she is a member of any other four orders or an apostate who wants to wait rather then tell what is relatively a total stranger something like that.
Beyond just standard Mage paranoia, every order has reasons to keep some of its membership unknown, some more so then others yes but it does not eliminate the possibility.
Vincent Winter
Xisdor Philip Crosen
Orianna Aurora
Fedup Corn
Delatdream Witch
ragnarokxg Eidolon
Stray Joyeuse
Miliham St. George
Lionell Salem
ReubanBrightwood Chambers
Skye LadySin
Asclepius Jombot
Guru Shane
Lachesis MaxPosh
Phoenyx Xadun