Regardless, the only number we have is from Microsoft, which is true of every single first day number we've ever gotten. The retail tracking sytems report weekly in Japan, weekly in the UK, and monthly in the US (although, it used to be weekly up until the end of March 2002 in the US).
If we took Squares, Nintendos, EA's, or Sony's numbers, we have to take Microsoft's as well.
November NPD won't prove or disprove Microsoft assertions and they are essentially guaranteed of having over 2.5 million units sold for November in the US (probably over 3 million easily, and it could be much, much more), which is so far past the number of units sold is a single month that it isn't even funny.
Biggest selling initial months for games this gen (US NPD)
GTA:SA 2,053,983
Madden 2004 (PS2) 1,445,950
GTA: VC 1,412,429 (although second & third month were 1,452,729 & 1,581,519)
Madden 2005 (PS2) 1,112,588
MADDEN NFL 2003 (PS2) 930,329
ZELDA: THE WIND WAKER 826,352
DRAGONBALL Z: BUDOKAI 787,173