We changed the oil ourselves but I am unable to locate the receipts to prove this.- This is your problem. If you can't prove you did maintenance they are going to say it was due to neglect, and most manufacturers would take this same stance. Especially when you put 32K miles on your car in only 11 months. Unfortunately because of the lack of documentation it is up to you to "fight" for it to be covered under warranty. So you are going to have to show that you didn't neglect the maintenance. For a repair of several thousand dollars they are not going to just take your word for it.
32K miles in 11 months would be considered high by most peoples standards. So hopefully you were following the "recommended" maintenance based on miles and not time. Based on this you probably should have been changing the oil about every month, so it seems hard to believe that you don't have a single receipt.
Also, you also should have been doing more than just changing the oil. So unless you did ALL of the maintenance yourself you should be able to show at least some receipts from shops. They may not have been for an oil change but if you have other records it could show you were not neglecting it.
How did you pay for the oil? Was it on a Credit/Debit card or by check? If so you should be able to pull your records showing you made purchases at an auto parts store that may show you bought the oil. Does the store you bought it from keep records? If so can you get it from them?
But if you have NO records then yes unfortunately you may be out of luck.
Have you taken it to an independent shop to see what they say?