It seems like there's a lot of DMs who are concerned (i.e. frustrated) with the subject of story in their games. This is egotism. Before you click to another page and completely shut this old fart down, let me explain.
I've read through MANY published modules and identified suggested stories/encounter setups. Just because a module's encounters read like a story, doesn't mean that's going to be the end result at the table. Ultimately, it's not gonna play out that way, and if it does, it's because the DM forced it or railroaded it. Story is created by the acts of player characters and, to some significant degree, their die rolls. And that's okay. In fact, often times, it's just as interesting - or more so – than that of the published adventure.
Some people forget that a DM is supposed to be a referee first, unbiased and neutral, not the next R. A. Salvatore. If you are that enamored with your so called story, write a book, don't DM a game. This goes for Do It Yourselfers too … you are creating scenarios and encounters that each player is going to react differently to. Don't try to control that … it just makes for disgruntled gamers.
Giving the players the freedom to direct the game will absolutely not produce the results you were looking for … and that's okay too. It's THEIR story, not yours, Mr. DM. Giving the players the freedom to be masters of their own destinies may require a little more work/preparation for the DM … players can be a tricky lot. Learn to improvise with the materials you do have ready or reasonably make it up on the fly – but be fair, unbiased, and consistent.
When Dming, I love it when the players take the reins; they are invested in the game, not some manipulated plot device. Being surprised as a Dm is honestly thrilling, so don't be afraid to reward players for amusing you. A little positive reinforcement encourages players to keep on playing their characters as people – sure, imaginary people, but people with their own goals and aspirations.
In the end, all we have are stories … but not before play finishes for the evening.