I think that opens up a complete can of worms, as some have stated before. I think it would depend on whether
1. You consider rules as a defining mark of whether a game is D&D or not, or
2. Whether you consider whatever simply has the brand name attached to it as D&D.
If it is #1, then you probably would not consider anything after 2e as D&D or AD&D, and in some cases you might not even consider 2e as D&D (though 2e DID have the grandfather clause officially put out by TSR that said 1e rules could be grandfathered into 2e per your own houserules and needs (aka...use 1e but take from 2e what you want - Or vice versa).
In this instance, 3.X is a different game than D&D and simply got the name attached to a different set of rules. You'd be very happy to label it as D20 Fantasy, or Pathfinder, or whatever name it is, but it still wouldn't be D&D really.
You'd also probably say 4e is definately NOT D&D. Afterall, though it has the branding, it doesn't have the rules.
There is that odd bunch that claim 3.X was D&D but not 4e...which is the confusing bunch to many, most probably got their start with 3e or came back via the 3e years to D&D, and hence aren't really aware that 3e has some truly far reaching rule differences from the original AD&D (though closer to late AD&D 2e, especially without the grandfather clause tossed in).
The differences between 3e is even more incompatible from D&D then the differences are between 4e and 3e (aka 4e is MORE compatible with the ORIGINAL 3e by WotC, than 3e was with the original D&D).
(a) They would distinctly break the rules of the above two points...but then those two points are regarding those who WOULD NOT consider Pathfinder D&D. For these people who consider 3e as D&D, and NOT simply because it had a brand name attached to it...a NEW rule discussed below must be applied.
IF it is #2, it doesn't matter what rules are out there, as long as it has the D&D brand name/trademark on it. Hence OD&D was D&D. D&D 1e was D&D. 2e was D&D. 2.5 was D&D. 3e was D&D. 3.5 was D&D. 4e was D&D.
Hackmaster was NOT D&D. Castles and Crusades is not D&D. D20 (anything) isn't really D&D. OGL (whatever) is not D&D.
This also means that Pathfinder is...not D&D.
Both members of #1 and #2 can like Pathfinder, enjoy Pathfinder, but are probably very happy to separate Pathfinder from D&D in rules, name, or both. For them it is it's own separate game, and they are happy about that.
Now there is another group...that group are those who consider Pathfinder D&D. They do not fall into the two groups that consider pathfinder it's own game.
Many of these would be...
(A) Those that think rules define the game. They also have a broader scope of rules that they consider define what is or is not D&D. They consider 3e as much D&D as previous editions, but consider the changes to 4e (though less drastic than those of 3e from core AD&D...truthfully) as the point that broke the camels back. This was the point that enough sacred cows were killed that the game could no longer be called D&D.
Hence, pathfinder shares enough rules, and doesn't break enough sacred cows of D&D...hence it still IS D&D. For them, Pathfinder IS D&D.
In a broader sense, if they go on to consider some D20 and OGL products and how closely those products hew to the original rules...they could also consider Castles and Crusades D&D, D20 Modern D&D, Star Wars RPG by WotC as D&D, Paladium Roleplaying as D&D...etc. It is truly dependant on their personal definition of which rules actually define D&D.
B. Those that feel intent of what the game should be, or is, defines the game. Hence for them they feel that the intent of 3e was to bring back the feel of the original game, but with some modern ideas (though not necessarily better...just more recent) brought to the game table. Thus the intent of 3e was to be as D&D, but modernized and made for them. It's the feel of the game, rather than the exact rules. The creators of 3e didn't go out of their way to destroy D&D per se, but to cater it to a broader audience and to sell it, at least for their mindseye.
In that light, Pathfinder could theoretically be the spiritual sucessor of D&D. For them, Pathfinder could be D&D.
D20 (whatever) is not, the spirit of the game is different...the feel is different. The same would go for Star Wars D20, it's a different game. However Pathfinder is basically the EXACT SAME game. It's a continuation of their favorite game with a few tweaks. For them...Pathfinder IS D&D. (Then again, in that light I suppose one could consider Castles and Crusades D&D, and possibly a few of the Retro clones, but NOT ALL of the Retroclones).
This hopefully didn't offend anyone, nor make anyone upset. Hopefully they found one group listed they can identify with...and see how different views can make and define how different people talk about Pathfinder when considering whether it is D&D or not.
In that light, I wonder which group would you fall into ...1 or 2...or A or B.
Maybe you're a hybrid of 1a, or 1b, or maybe 2a or 2b...or maybe you don't have a group....
I'm thinking the 4 above types (we could even call them type 1 personalities or however we want, etc., etc., etc.) would include a majority of people and their ideas on this matter though.
Hopefully it addresses the different groups respectfully and nicely. Everyone is different and thier opinions are different to. That's just how the world flows at times.
Now can't we all just get along.
Personally, I'm happy just to call Pathfinder as Pathfinder and have those rules have their own distinct individuality as it's own game...rather then confuse people by calling it D&D and have them end up bringing other D&D books to the table (whether they accidentally bring 1e PHBs or 4e PHBs...when you say Pathfinder...thus far there's only ONE book they need to bring for that...no confusion there!).