What draws the people who make thrillers to "Bolero?" That is, beyond its popularity and recognizability? It's not it's cheap. Unlike, say, the opening of Beethoven's 5th or another equally recognizable piece of music, "Bolero" remains in copyright (and that's part of the reason Maurice Ravel's estate earns more in royalties than any that of any other composer). Ravel himself joked that "Bolero" was "a piece for orchestra without music." What matters in "Bolero" more than the simple melody is the same thing that matters more than plot in a thriller: construction. The importance of a plan and the careful organization of elements. It's possible to build a great thriller out of an obvious set-up and a lame twist, and just as possible to squander an excellent scenario by assuming that plot in and of itself is thrilling enough.
Like Femme Fatale (released 4 months earlier and shot, like this film, in 2001), Basic opens and closes with "Bolero." And, like Femme Fatale, the ending of Basic invalidates most of the plot of the film as we've understood it up to this point. Which doesn't, in either case, mean that everything but the last ten minutes of the movie "didn't matter." If, like me, you think that both Femme Fatale and Basic are great movies, then they both also seem like object lessons in the value of construction over "plot" -- the elements of both movies don't add up to much of a story (in fact, in both cases it's revealed that the story never happened; each film's cynical narrative is negated by a Utopian ending), but the arrangement of those elements is a completely different matter.