Don't tell the 4e fans that its focused on combat, they get grumpy about it.
Not at all!
Clearly, in 4e, combat is the
preeminent site of conflict resolution. It's just not the
only site of conflict resolution. And nor is the game
about combat. (I compare it to classic X-Men or Hulk comics: combat is the preeminent site of conflict resolution, but neither is about combat. X-Men is about social liberation. The Hulk is about Freudian psyhcology.)
When I'm running a 4e combat, I find the profusion of fiddly bits slows us down so that its easy for me to drop out of the narrative head-space and into that "tactical skirmish" mode.
That's why I try to use the combat to express/progress the story. (OK, so it's a pretty violent story.)
That's also part of why I talk about my game being "light". In the last session, the PCs (led by the dwarf and his dwarven thrower artefact) had assaulted a small fort with goblins and trolls inside it. The whole thing was poorly planned - the players were expecting a walkover and were overly cavalier, to the point that they had even checked how they would all get through/over the walls, and it took the paladin about 3 rounds to get in, and the invoker more than that.
Anyway, the fort had a tower attached and it became clear pretty early on that some psychic being was inside it (because of telepathic communications, plus psychic attacks through an arrow slit). The drow chaos sorcerer flew up to the top of the tower to try and find a way in and deal with the psychic - who had been generally identified as a mind flayer (via a combination of reasoning from established ingame law, plus one of the players correctly guessing that I would find mind flayers pretty cool).
So while everyone else is down in the fort fighting goblins and trolls, the sorcerer is on his own, on top of the fort, opening the trapdoor to take down the mindflayer solo. And one of the other players even says, "You're crazy, and if your brain gets eaten by a mindflayer I'll laugh." Needless to say the PC sticks his head down the trapdoor, gets grabbed by tentacles and then "Bore into Brain" begins, while the other PCs are down below fighting the "real fight" and wondering where the hell their main artillery support has got to.
I didn't get to actually eat the brain, because the ranger-cleric (whose player was the one who threatened laughter) climbed up to the top of the tower and used healing magic to keep the drow alive. (I was planning to go for the "dominate" option, because that sorcerer is awesome against the other PCs when dominated.)
That's story, of a fairly basic kind, and the way it played out was very consistent with how the PCs play and what they are built to be and do. The drow especially is the instigator (at the character level as well as the player level), and is built for it.
Now that's a story that could play out in a lighter system too, but something about the fiddly bits - knowing how many turns help is away, watching those hit points count down as the mind flayer tries to crack the drow's skull, etc - creates some sort of viscerality. Maybe I've just got very traditional sensibilities.