The last time I heard of someone buying an iPhone in a non branded box, she ended up getting a box filled with potatoes. Your wife is already ahead on that person.
Actually it's pretty standard to get replacement phones in a plastic bag with no accessories, I got a 5S replacement in a ziplock bag with a piece of A4 paper with some diagnostics data printed on it all in a thin layer of bubble wrap then in an envelope. All standard for Authorized Apple resellers and service centers in Eastern Europe, idk in other parts of the world. I'm guessing an official Apple store doesn't do that.