Might just be easier to bring the box? How hard is that?
Maybe you care to know more about the situation.
I had an iPhone that was going to be exchanged for another one, and I was told by two employees that I
absolutely needed to bring back the box, despite telling them (among various other reasons) that not only was it infeasible to bring back the box the same day as the store was going to close in less than an hour and it would literally take that much time just to get out of the parking lot, but also that I didn't have the time to do the whole process until days later when it might be questionable if the store even had 8gb iPhones in stock (right now, they don't have any..). But because I had already spent so much time on this and I am already here I might as well take home a replacement because they did have one available (although not soon after, much to the frustration of some customers).
Why didn't I take the box with me if I knew I was going to the genius bar? I made the concierge appointment at a different apple store after I was told there that I should get that looked at, and I didn't have much time to go back home for the box given that there was so little time to go to the genius bar and get my problem dealt with before closing time as is, let alone if I went back home for the box. Apple never gave me a hard time about the box ever, so I assumed this would be the case with the iPhone.
The third employee who helped me thought the whole thing was BS and outright told me that I shouldn't bring it back because he never asked for the original box from the customers he dealt with earlier who also didn't bring their boxes for whatever reason, and he had never heard of such a thing either. I should have listened to him, because it turned out that they used the new box for the old phone in the 15 or so hours between the time I left the apple store with the new phone and the time I came back with the old box.
Virtually everyone else, including the manager who called after I complained about the issue to executive relations, said they never require the original box.
Hence, why should I go back home and spend an additional hour to bring back a box with a particular sticker with a particular serial number on it if they have NO problem using the new box with the old phone? Apple Stores have almost no issue with people who forget to bring or lost receipts/proof of purchase. They also have no problem doing this for other Apple hardware. Why was the iPhone an exception?
Obviously if you are in a situation where it is possible to take the box with you, it would not be a bad idea. But when you are not, for whatever reason there is, there's no reason for any Apple employee to make you go get the box.