See, this has always been my opinion about stories and video games. I only think a story can really be considered detrimental to the experience when it is constantly being shoved in your face.
I know mentioned Epic as being guilty of producing games where this is an issue, but I would disagree, at least for the first Gears of War. The story was very basic and fairly dumb, with none of the characters being particularly likable and a number of stupid moments. However, to me this was never an issue because the story just felt like a way to move you from various locals and engage in more gunfights. They never had a long, lengthy cutscenes which unloaded tons of exposition onto the player. Whenever they did yank control away from you, it was just to explain why you were going to another area and what your goal was. So while the story was bad, it didn't ruin the game since it didn't keep me away from the game play.
Compare this to Tales of Symphonia. I complain about this game having a horribly dumb story a lot, but that's only because it really does become detrimental to my ability to enjoy the game. While I think the game play is great, the fact that I have to keep sitting through long cutscenes and listening to exposition I don't give a damn about irritates me. If the cut scenes were short and got straight to the point, it wouldn't be so bad. That's the advantage that Gears of War has over Tales of Symphonia. Both have bad characters and dumb plots, but one of them has enough sense to keep it tucked away most of the time and let you enjoy the actual game rather than make you slog through painful dialogue.