My local (Iota Beta Chi) doesn't let any non-initiated sisters wear letters. And yes, the reason is because they don't know what the letters stand for. Once they become sisters though, we get their big sisters to lend them their sweaters for a photo shot.
They are allowed to wear shirts with our letters spelled our, or with IBChi on it, just not IBX! All of our girls seem to respect that....and are very happy and honored when they are finally allowed to wear the letters for the first time!
FYI...we also don't let our girls write our letters until they become sisters...for the same reason, they don't know what the letters mean. We also don't allow ANY of our sisters to write the letters of other greek org's for the same reason! We either write their nicknames or write the letters out in full!