"setting the backdrop" is correct and can be used in written English.
You can use it to describe something that serves as the foundation or context for a larger story or narrative. For example, "She began the presentation by setting the backdrop for the project's history."
"With the Chancellor [George Osborne] setting the backdrop to this afternoon's Budget as one where the global 'storm clouds' are gathering, today's labour market figures offer a ray of sunshine," said Scott Bowman, UK economist at Capital Economics.
The trio were listening to music such as Jawbreaker, Bad Religion and Lagwagon, setting the backdrop for the recordings under guidance of Mark Trombino, who provided additional piano and keyboards on Dude Ranch.
With the tragic spectacle surrounding alternative spaces setting the backdrop, a light art and experimental music showcase I had spent the entirety of fall planning at a friend's loft space in Bushwick was selected for a review in The New York Times.
With the 25th anniversaries of the CRC and coincidentally of the World Wide Web setting the backdrop in 2014, UNICEF is joining forces with the Malaysian Communications and Multimedia Commission to empower children and youth in Malaysia to use digital media safely, responsibly and in a pro-social way to create positive change for themselves, their peers and their communities.
The recent budget sets the backdrop.
Trees, shrubs, perennials all join in, and the stage is set, the backdrop perfected, for the season's flowers.
But many strategists say that the outcome of the debate over the shutdown is important because it will set the backdrop for the battle over the debt ceiling.
Washington's new political landscape set the backdrop for presenters focused on how national issues will play out in the West.
As suggested by the question to Mr. Ferrer, the attack on the World Trade Center set the backdrop for the debate between these two candidates.
A peeling mural of Muhammad Ali and Joe Frazier sets the backdrop to the fight today, which promoters have dubbed "The Thrilla in Manila II".
However, they said, the recent Republican gains have perhaps set the backdrop for the emergence of an angry liberal who could claim the same outsider status that worked so well for Mr. Limbaugh in the early 1990's.
