"From a larger perspective, the Saudis are trying to curb the influence of radical, violent Islam..."
Wahhabism.
For more on the background of this I'd recommend
Jihad: The Trail of Political Islam
by Gilles Kepel (Author), Anthony F. Roberts (Translator)
http://www.amazon.com/Jihad-Trail-Political-Gilles-Kepel/dp/0674008774
Amazon.com
Gilles Kepel's Jihad is an intense, detailed examination of the militant Islamist movement over the last quarter-century. Kepel divides his book into two parts--"Expansion" and "Decline"--and posits that the September 11, 2001, attacks, rather than demonstrating "strength and irrepressible might," highlighted the "isolation" and "fragmentation" of a "faltering" and probably doomed extremist ideology. Kepel follows Islamism from its theoretical underpinnings in the late 1960s and its rapid expansion into Africa, the Middle East, the Balkans, and Central, South, and Southeast Asia, through the Taliban's ascendancy in Afghanistan and beyond. He explains Islamism's attractions, and outlines its severe shortcomings. With consummate skill, he illuminates the bewilderingly intricate effects global events (oil prices, the fall of Communism) have had on internal politics of individual countries, and vice versa. Kepel, wisely, refuses to prognosticate. Instead, his achievement is in providing--for the determined reader--a deeply authoritative context for the seemingly inexplicable events of the recent past.