Attempting to return a pair of shoes without a box puts the retailer in a tough situation because both checking the item back in and then selling it in the future become difficult, if not impossible.
No Identity, No Sale
Without its appropriate box, a retail clerk cannot scan the item back into the store's computer system unless the exact same style and size is found in stock (every item has a unique UPC code). Even if this can be done, it is most likely not possible to acquire another box in which to re-sell the item (unless another customer has returned a box sans-shoes).
Shoes "Used" Already
The store also cannot be absolutely sure the shoes have not been worn. If the item shows any signs of wear, the retailer cannot sell it as "new" for the full price. The retailer's only options would be to sell them as used or return them to the manufacturer.
They're Not A Pawn Shop
From the store's point of view, the shoes could be stolen from anywhere. This is a regular scam, and prevents you from receiving the benefit of the doubt. Companies do not want to be held liable for peddling stolen merchandise. If you don't have a box, you probably don't have a receipt, and nobody will be able to prove the shoes aren't stolen.
- old gym shoes image by robert mobley from Fotolia.com