NOOOOOOOOOOOOOOOOOOOOOO!!!
You don't really NEED proof of purchase on something that has a lifetime warranty, although I don't believe all Greddy exhausts do have one.
First off, call the shop you got the muffler from initially and see if they can locate your proof of purchase. If they cannot find it, have THEM call Greddy to discuss the situation. Manufacturer's are more likely to work with distributers than customers when it comes to grey areas like lack of proof of purchase. Greddy has your money already, but they continue to make money every day off of distributers and they want to keep that business.
Ultimately all waranties come down to proof of purcahse, and without one there really is no warranty, even if it is life time. Product warranties only apply (in general) to the original purchaser unless they are transfered in writing through the OEM to a new owner. No receipt = no proof that you bought the product or are the original owner. For all they know, you bought the exhaust system from someone knowing that it was bad with the idea of getting a new one by playing the system.
But at least TRY harder, have the shop call on your behalf, or in worse case, you call Greddy back and see if you can get someone else on the phone who is more willing to bend the rules a little. Why pay money for a new exhaust system when you should be able to get yours replaced for free?