There are a host of reasons why Apple's attorneys would argue for this limitation:
1) Used merchandise is typically sold "as is" with no implied warranties. (Of course, existing warranties can be transferred, but that's a different story.) Basically, you assume ownership of said merchandise at your own risk with no guarantee from Apple or the previous owner. Caveat Emptor.
2) Used merchandise is typically sold at a discount. You're paying a lesser amount because you already assume the product isn't in the exact same condition as it was when purchased from the retailer. Therefore, Apple cannot be expected to offer award money or replacement products to second-hand buyers without opening themselves up to fraudulent claims because A) They don't know the condition of the used product when it was sold; and B) Second-hand rev. 1, 2 and 3 iPods sell for widely varying dollar amounts and the award offer could easily exceed the amount paid by the second-hand buyer. Any award offer would be worth more to a used buyer than to an original buyer.
EXAMPLE: If I bought a NON-WORKING iPod on eBay for 5 bucks, should I be eligible for a $50 check from Apple?
EXAMPLE: If I figured out which revision 1-3 iPods carried the higher awards, what's to stop me from buying all of them up on eBay and cashing in? Show me where to download that "sworn statement" document and I'll stamp my signature as fast as my printer can spit them out.
You think Apple should be more forthcoming? Just look at the number of jackhole posts in this thread where owners of perfectly good rev. 1, 2 or 3 iPods are trying to figure out how they too can cash in on this award.
Yeah, I'm not sure yet if my 3rd gen. iPod problems qualify, but just as a backup maybe I'll fish around eBay and see if anyone has a fingertip they'd like to sell...