I've seen a number of games where the game play was focused more on rules than story. However, you can have just the opposite problem as well - story overriding the game. That seems to be what's happening here.
Role-playing is a communal experience. It takes both players and DM to craft an adventure. The DM sets the stage, but in the end, the players are the actors. That can be tricky at times, as there are so many different types of players. One player can focus on storytelling, while another player can focus on combat, while a third can focus on puzzle-solving (and so on and so forth). The DM needs to provide something for all of these types of players.
The DM has to realize his role in all of this. His responsibility is to provide the players with a good time. He's part storyteller, part puzzlemaster, part entertainer, and part magician.
Part of this overall duty is to have a good understanding of pacing. I'm a firm believer of using pacing to enhance a game. If it's going too slow, throw a monster in. If there's too much fighting, throw in a puzzle, trap, or some roleplaying. If your party is split, know when to go between groups. Leave one in suspense as you go to the other one (kind of like a TV show).
It's a tough job! You have so much to balance.
In this particular case, the DM is forgetting his job as entertainer, and is focusing too much on story. He's forgetting that the players control the characters, not him. They are the ones who drive the story.
Rules systems are independent of role-playing. It's the players that bring the RP to the table. I'm running a very story-driven 4e game right now, and it's a blast. 4e is no more to blame for bad role-playing than 3e or any other edition or game system is. So it can be done.
I like the advice given in the thread about volunteering to DM a game sometime. Maybe the DM in question just hasn't seen another way. However, if that doesn't work out, don't be afraid to say, "Hey, I appreciate the invite, but I don't feel that our play styles mesh the best, so I'm not going to continue. Best of luck to you." I made the decision once not to game with some friends since they do mercenary-style games and I like heroic games. We're all still friends, so all is good.
Best of luck on this issue.