If you pay the balance in full every month - you have spent $2000 on a $2000 mattress by the end of the month. This exposes you to ~30 days of inflation and you will have paid no interest.
If you pay 0% APR over a twelve month period, and make installment payments until making a single lump sum to close out the line of credit at the end of twelve months - you are exposed to something closer to ~365 days of inflation (depending on the installment payments and the lump sum). You will have also paid no interest.
If we assume roughly 7% yearly inflation, you're paying less real value if you take option number two, because you will have paid $2000, but that same mattress is now worth ~$2140 - You are abusing the time differential between purchase and payment to receive a discount.
That said - this is not the majority of folks using these services.