Just went back to the link and it works - provided the purchase date is on record. I'm in Australia checking the US site so it's not region-specific. It seems that Apple does not have your purchase date on record and therefore cannot give a statement of validity.
I bought my iMac through an Apple store in Melbourne, although it was actually an online order as they directed me to a customer-use Mac and I had to sign in with my Apple ID and order from there with higher specs than they had off the shelf. Your experience I presume was less well recorded.
I have been looking for the page where you can upload your proof of purchase so that it can be added to the device on your Apple ID account. The only one I could find was for Apple Care which is about half-way down this page, under "Learn more about updating Apple records". Not sure if it's the one to use.