When you register a product in CPS, you only need a serial number and there is no info for where you bought from and price etc that are in regular Canon product registration. I also called Canon CPS (as a CPS member) twice before and after I bought 5DIII from BVI. They told me the same that Canon simply has no policy that you must buy from authorized dealers to be covered in warranty or post warranty services as there is no such item in End User Agreement, period. However they do insist theoritically they can ask a copy of USA warranty card but in reality all persons I spoke to say in reality they usually don't ask as I experienced in person when I sent my S95 (lens unable to extend) and 60D (rubber peeled off around shutter) in services during warranty, I was never asked to include a copy of USA warranty card but only a copy of receipt to prove it's purchased within one year from a company registered in USA. Both Canon USA and CPS told me that they no longer be able to tell a product is USA or grey imported based on serieal number. Canon USA guy even told me they usually also cover imported grey products in service as courtesy.
Anyway for this 1DX I'd buy if I need 1DX if there is a USA warranty card regardless if it's authorized dealer or not that is really irrelavent. I am very happy on my purchase of 5DIII on that unbeatable price