I've merely quoted the books.
Ultimately it comes down to DM ruling, but it should, I think, represent the situation.
In my opinion, allowing this best helps a mage character, although the way it is written allows rouges to take advantage. So long as said rouge is okay with being a walking beacon for anyone with detect magic...
However it also depends on the nature of magic in the campagin, the interpretation of a cloak as either 'garment' or 'armour', etc.
Hope I'm being helpful.
Note: I normally make such items rare, thereby avioding this scenario.
Plus cloaks allow me something to use against my players... they dont trust them anymore