Nowhere in the Terms and Conditions does it say that only new Macs are eligible. The only instance of the word "new" is in the title at the top of the form, and the context would imply that "new" simply means that it's new to you, not necessarily a brand-new item. Regardless, it's what the T&C says that's important.
So technically it would be valid on refurbs. Whether or not they'll give it you is another question, and how far you're willing to take it is yet another. I'm confident you'd win in small claims court against them, but it probably isn't worth your time. If you think they'll cave in early or that you're just more stubborn than they are, go ahead and give it a go.