Fifth Element
Legend
When someone says "4E is D&D", they don't mean "4E is the entirety of what is D&D", and to say they do is disingenuous. They mean "4E is legitimately included in the group of things collectively called D&D", which you agree above is correct. I know this is so because "4E is D&D" is generally only seen as a response to a claim that it is not D&D, in the sense that it is not a part of the group of things collectively called D&D.D&D is a series of individual games bearing the name over the past 3 decades. No one game in the series is wholly D&D. Therefore while 4th edition may carry the name of the newest game in the series, it is not all inclusive to defining D&D. Therefore 4th edition is not D&D but a part of a greater whole of the individual games over those decades that has bore the name of D&D.
4th edition is a D&D, but 4th edition is not all D&D, so saying 4th edition is D&D is false.
So when you (specifically you) say "4E is not D&D", you get flack because people read it to mean "4E is not part of D&D". Because you only say 4E is not D&D. You don't say "3E is also not D&D, 1E is also not D&D, etc", which would be true according to your definition above.
But then we get the confusion because you say that OD&D is D&D, as is BD&D. So you mean it in a different sense there, meaning only games literally named only "D&D". But then that's not right either, since the game we call 4E is actually just called "D&D".
So in summary, you seem to mean different things with the same words at different times, and you use these words in different ways than everyone else. Which leads to your posts causing a great deal of confusion amongst those who read them.