It's simple. Prove your story and sign the message from one of the original addresses you used to make the transaction. If you are unable to do that, then there is no reason to believe your story over a legitimate business.

It's obvious they have no intention to scam since they have already expressed their intention to return the coins to the sender's address. Too bad you don't have access to that wallet... and that your plan backfired. Better luck next time.