Designer Shoe Warehouse [DSW]

I purchased a pair of shoes at the DSW store at Pentagon Row in Arlington, VA. I wore them probably five or six times after which a seam on the side of one of the shoes started to come apart - about an inch long gap appeared.

I took them back to the store to exchange them for a non-defective pair. I was told by the manager that the shoes could not be returned because there was no way to know whether it was a manufacture defect or whether I "wore the shoes wrong" - as if there's an improper way to wear shoes (put them on my hands? wear them backwards?). I told her I didn't abuse the shoes in any way, but she said she still couldn't take them back because I didn't have the receipt.

So which is it? Is it the store policy to not accept returns without a receipt or would having a receipt not made a difference because even then they couldn't determine whether the shoes were defective or whether I "wore the shoes wrong"?

Regardless, I think this is an awful store policy. If I had bought these shoes at any department store across the street at the Pentagon City Mall I could have brought them back and they'd have exchanged them for another pair. The store would then send the shoes back to the manufacturer and receive reimbursement. Why can't this be done at DSW? Instead, I'm stuck with a pair of defective shoes and I can assure you I won't be shopping at DSW anymore.