After elford's excellent description -for which I thank him again - I can accept the increase in DR when downsampling.
I will also accept that Nikon has greater DR but we have to think of it either as a 36Mpixel camera with 13.2 stops DR or a 8 Megapixel camera with 14.4 stops DR (which makes it practically a different camera, otherwise someone would downsample to what 2Mpixels? Wouldn't that increase DR to say ... 15 stops?)
It is NOT a 36Mpixel camera with 14.4 stops DR at max resolution (we cannot have the cake and eat it!) So if we want to think of D800 for what it is mainly (a 36Mpixel camera) we have to think of it as a 13.2 stop DR camera. (This does not reduce the DR capabilities of D800 of course).
P.S Too much trouble and fights. What is a 1.2 stops difference in DR between forum members?
The intuition is about right though it's really best to think of it as 13.2/36mpx, and then think of 14.4/8mpx as where you'd go if you could extend the DR/resolution tradeoff all the way down to 8mpx. It's useful if you want to compare two cameras with different resolutions
The full story is a bit thornier than that. You can't push the black point more than 14 stops lower than the saturation point, but you do keep getting cleaner shadows as you downsample (e.g. down to or even lower than 8mpx) which means more usable