Yes, you're right. It absolutely it should have been removed. Either she did not realize this or she thinks it's a status symbol, much like someone who buys a new car and leaves the sticker price in the window for much longer than they should. (Hey look, I spent X dollars on my sweet new ride! Aren't you impressed?" Um, no.)
The only time I have seen anyone unclear about leaving the tag on a jacket was when I was working in men's apparel and a lot of young men - who had never owned a suit before - were confused about what that label was for and whether or not it stayed on the jacket cuff. (The tailor always removed it for them.)
