Actually, that's exactly what you are saying. If the warranty is limited to the original owner, you are not the original owner, and you are claiming to be the original owner, that is the very definition of fraud. I personally would not be comfortable claiming that I bought the regulator at Authorized Dealer when I in fact bought it from Joe Blow.
When I bought my last Atomic M1 at Pan Aqua Divers, an authorized Atomic dealer in New York, they took my name, address, phone number, etc., and if I remember correctly, included all that information on the receipt. That is what I meant when I said, "they could require a receipt in your name." I guess they would sell you an M1 for a wad of hundreds, even if you refused to identify yourself. I wonder how they'd handle the warranty in that case.