Sure, different. When you want a game of type "X" you use game "A", and for "Y" you use game "B". Its always been that way. Sure, there are also 'framework' systems like GURPS, FATE to some extent, d20, etc, but they never deliver the same level of focus on tone, genre, setting, or agenda like a specific game does. Just adding modules to a core CAN go some ways, but not all the way, not even close.
I fail to see how a FATE implementation like Legends of Anglerre or Dresden Files fails to deliver the same level of focus that a game like D&D does. Creating such an implementation is rather trivial.
Well, this is also a very hard conversation to have in a vacuum. Look at DDN's design and tell me that you would make a highly reskinnable game with a narrative agenda and an encounter focus out of it. Is it possible in some way? Sure, if you rip out 99% of the rules and replace them. At that level of customization nothing is really common.
Agreed about the vacuum.
Reskinnable? To some extent, sure. Certainly one could re-interpret DCs and the like to adjust "gonzocity". I'm not sure that I care about it being re-skinnable beyond its fantasy wheelhouse. I don't find that a particular virtue in a system, except for universal/generic systems, of course.
Narrative agenda? A little tougher, but can be added to a baseline old-school D&D with a modified alignment/XP system.
(see below)
Encounter Focus? Trivial by adjusting the adventure design rules. I fully expect to see that come up as they have already talked about making the "recharge" trigger DM-determined.
I don't think Mike is saying that 4e IS bound to some narrow tone/genre/etc but that it has been presented and perceived that way. It is impossible to know what he thinks about the actual flexibility of the system. However let me ask you this, in what way is 4e less flexible than 1e or 2e? I see no evidence whatsoever that it is. Saying that "all the existing powers are designed for a fantasy action hero game" is all well and good, but in that case 3e is all about a high magic fantasy game of powerful wizards, yet somehow people managed to use it for other things. I've so far seen 4e WITHOUT mechanical changes, just reskinning, used to do a Star Wars game and a Super Hero game (literally using the races, classes, weapons, powers, etc of 4e right out of the book, characters can be built in CB and then reskinned, no numbers change).
Your choice of examples is telling, whether you see it or not. The type of action that 4e was targetting
includes the type of action you see in Star Wars, and people often refer to 4e's tone as "super-heroes". Changing between them
is a fairly straightforward "reskinning" or re-coloring. Trying something like Game of Thrones or Black Company is more difficult. You're right about 3e, too. The difference is that its just easier to adjust that tone with 3e, as you seem to admit(?). Mostly because....
With new classes and powers it can certain do much more than that, and with slightly deeper changes (different skills, alternate subsystems of various types) I think its pretty clear you can do a wide variety of things.
...doing this is much harder in 4e than previous editions. Consider what that means for the different systems. If I want to adjust magic, or combat, or any other feature of the game....I can take 3e and do that by adding some feats, changing a few rules about initiative or combat casting, etc. Because of the structure, I can make changes to the tone of the game by directly addressing it. Now to do the same in 4e...well just consider what it would take to alter the tone of melee combat....all those powers to review and modify... In which system is it easier to generate a new class? If, as I am often informed, the powers and their functioning (all the X's and O's) is a necessary vehicle for the 4e architecture to convey tone, reworking the tone of melee combat would require examining and rewriting hundreds (thousands, by now?) of melee powers in multiple classes. I think sheer proliferation of classes, feats, spells, etc. in 3PP and on the internet argues for 3e/d20 there. In the older systems, things are even less structured.
Which is not to say that older editions were some universal system...far from it. However, the less narrative specificity the mechanics incur, the more is up to the table to invent. For any of the systems in question, the amount of work required is proportional to the deviation from its "home" tone and feel. Its just that slope of those valleys differs between the systems. I'll go a step further and point to a game that I suspect would be even harder to bend away from its native feel than 4e would be: Dungeon World. Reading the notes about how they developed the moves for the various classes...wow...at least 4e gives you a core mathematics to work from as you crank out the powers. In DW, you'd have to test and re-test each new or re-worked power to see how it felt in play. (I could be wrong on that, though. Folks are cranking out new DW classes fairly quickly. I haven't heard much talk about relative quality, though.)
I've never heard of anyone doing narrativist classic D&D, certainly not before really narrativist games were released.
Sure you have.

They were called alignment restrictions and Paladins were/are the poster child for them, especially when a thief or assassin was in the party (or anybody evil/chaotic, in some versions). Of course, the old-school Paladin mainly faced the "stick" end of the mechanics. Gold for XP, and class-based XP rewards were a "carrot" to help push the thieves and assassins into conflict with the Pallys. Its a mechanic that drives players to confront a dramatic premise: Narrativist to the core. Above, when you asked if I could see adding Narrative Agendas to D&DNext, I was referring to this. Bolt on a more sophisticated and variable version and voila, you've got it. Coming up with the rules module for this wouldn't be exactly trivial, but its not impossible or even terribly difficult.
In fact D&D has become more and more focused on a sort of process-sim type of agenda over the years, if anything. It was at least pretty abstract back in the early days. So sure, in some sense it wasn't 'hard' to do some completely different agenda with say OD&D, but that was more because nobody could quite figure out what it was to start with.
No argument here, although many will argue that 4e breaks the trend towards process-sim.
The proof is in the pudding though, all those people went on and invented different systems. Heck, Traveller came out within a year of D&D and immediately invented a very different sort of skill based system (clearly it owes a good bit to D&D and is a very SIM agenda game, but the tone and other aspects are quite different and its mechanics specifically support them).
Yes. Once the basic idea of an rpg was out there, people started making other versions to better address things they wanted to see (with wildly varying degrees of success). That process hardly stopped or even slowed when 4e came out, so I'm not sure what you think it proves. Its not like 4e came out and suddenly all the other companies and indie designers closed up shop crying "Finally we have found the perfect Role-playing architecture!"