If you really had ordered it, they would have your personal information in their database, which is required when you first order it.
Unfortunately, when you call them, you are required to state your last name and zip code, as well as restate your billing address, so there might not be a way to dispute it if they managed to take all that information down.
Suggestion: Have them state (or fax) the invoice. When you allegedly ordered the product, the information provided, as well as the bank information. See if all of it matches. Give as little personal information about yourself as you can, so they can't use any more against you.
Is there any chance that someone used your credit card? Did you ever receive their product?
I haven't read the return/exchange policy, but if you have received the product, then perhaps you can send it back for a refund?