The phrase "according to this story" is correct and usable in written English. You can use it when you are referring to a narrative. For example, "According to this story, the knight was able to find the hidden gem thanks to the wise words of a magical creature."
According to this story, Thi's airborne units were initially moved into position for the coup without his knowledge.
Child delinquency is on the rise, according to this story.
It's certainly the most popular, according to this story.
District officials said that was planned before Schwarzman endorsed it, according to this story on philly.com.com
The Churchill thesis: According to this story, dire deficit forecasts are a necessary part of the political adjustment process.
So cutting the tax rate, according to this story, will bring in lots of capital from abroad.
The company also announced its plan to develop a portable digital video player, according to this Reuters story.
Thomas went on to say that governments are pushing to collect more information from credit-card purchases, mobile-phone use, and travel itineraries, according to this BBC story.
New 3D-graphics have enabled designers to retrofit the original games, giving them a shiny, up-to-date feel, according to this Reuters story.
The U.S. Air Force announced yesterday that it is developing "a major command aimed at safeguarding U.S. military and civilian cyberspace," according to this Reuters story.
Now, using an electronic payment system, parents can check up on the food their children are eating in school, according to this Associated Press story.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union