In 2006, after nearly a decade at CNN, Rudi Bakhtiar came to the Fox News Channel’s headquarters in New York with a command of foreign policy, an appealing personality and a delivery that easily switched between light and serious.

After a six-month freelance arrangement, the network signed her to a three-year deal. Pretty quickly, she said, she was spending half her time in Washington, where the network sent her to fill in temporarily as a weekend correspondent, a post she hoped to win permanently.

Her break seemed to come in early 2007, she said, when she met for coffee in the lobby of her Washington hotel with a friend and colleague, Brian Wilson. He told her he would soon become Washington bureau chief and wanted to help her get the weekend job. Then he said, “You know how I feel about you, Rudi.”

Recalling the encounter in a recent phone interview, Ms. Bakhtiar said she was thrilled and told Mr. Wilson she would make him proud. But, she said, he repeated himself, asking, “You know how I feel about you?” When she asked him what he meant, he said, “Well, I’d like to see the inside of your hotel room,” adding that he wanted a friends-with-benefits relationship.