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This is a naive question on my part, but why do you need the warranty card? I registered my 1Dx online with Canon to start the warranty period. If you have the option, which you do to register online and you have a receipt for the product, where is the problem?
It's true that, per many people experiences, myself included, a warranty card has never been required for warranty service.
So, why is it important to have a warranty card? What's the point? If it's not at all important, why doesn't Canon USA just drop it? It would have saved them quite a bit not having to print them.
The answer is obvious. When you buy a Canon USA product from an authorized dealer, it should come with a warranty card. That's how they distinguish their products from gray market. If a product doesn't come with one, you got to question why. Now, say, if it's indeed a Canon USA product, but the warranty card is missing, what happened to it? It's forgotten when packing or it's an opened box and got lost.
The more likely scenario is that the product is gray market and should NOT be covered by Canon USA.
But some people still say that Canon USA still fix it as long as you have a receipt from a US retailer. I don't know how many people know this, but that's the case. And that's why many people say you don't really need a warranty card. I believe Canon has something else to worry about, other than dealing with non-authorized dealers and warranty card. (The proper procedure for warranty card that is implemented in many other countries is like this. When you buy a product, retailer writes down your information on the part of the warranty card and submit it to Canon. But it's never been done in the US. At least, it's not a common practice.)
And that's how some retailers like BigValueInc take advantage of this loophole. They intentionally create a false advertisement that their products are Canon USA. (It's been discussed a lot when they listed several listings for 5D3.)
If that's the case, why should anyone worry?
Well, I would be if it's me. Why?
Based on Canon warranty statement (on any warranty card if you read it), Canon will only cover products that come with a warranty card. Well, basically, that's their legal terms. If you have a warranty card, no matter you buy it, they cannot refuse service.
In practice, you will never know for sure when in the future Canon will enforce this policy. It's probably unlikely, but you cannot be absolutely sure. If one day Canon starts enforcing the warranty policy and you can't claim it because you don't have a warranty card, don't blame Canon for it.