Interesting post on that "other brand" rumors site. They have a price list that shows the new Nikon D800 cost to dealers at $2,699.96 U.S. and the MSRP at $2,999.95.
I would expect the 5DIII to sell for essentially the same price as the D800. If Canon offers similar pricing margins for their dealers, I wouldn't expect to see much of a discount.