Well, here's a "mystery" solved, courtesy of The New Yorker.
At lunch today I read the article about Romance author Nora Roberts in the June 22 issue (yup, I'm actually caught up in my issues!). The article includes some discussion of the history of the genre, beginning with Samuel Richardson's Pamela, published in 1740. The discussion also mentions a novel called The Sheik, published in 1919 and described as '"the ur-romance novel of the twentieth century.'" The novel is the story of an aristocratic Englishwoman, traveling in the Algerian desert, who is kidnapped by an Arab chieftain.
OK, one of Rudolph Valentino's most famous movie roles was The Sheik. Now I suppose I know where the movie role came from; it was an adaptation of the novel--or maybe it was inspired by the novel to take advantage of the popularity of the book. I guess this also tells us that even in the Silent days, Hollywood made adaptations of current popular novels.