I don't think they require proof of purchase per say.
Whilst you could fill it out and send it to Specialized, I am dubious about if they would accept it because I thought that the bike shop you bought the bike from needs to stamp the warranty card and send it to specialized.
That is what happened at least when I bought my bike. The bike shop owner forgot to do it when I was at the store, (and his shop is far from me), so he posted the warranty card to me, and I had to send it back to him, and then he sent it off to Specialized.
If it is a used bike, then the official stance is that you get no warranty.
I look at it like, I pay more, but I get a bike for life. If in 10+ years time my frame develops a crack, or an ovalized headtube or something, then I know they will give me a new one. That is worth paying extra for a new bike.
If it is a 2008 model, can't you find any deals on new bikes, they must be blowing them out now with the 2009 lines in stock!
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