She’s already been caught in a lie, forced to expose her ploy to Kate. She was careless. But she can still salvage this. Jack believes her; Kate’s distrust can be written off as jealousy.
This man, Sayid, is more formidable. She must appear to break, to reluctantly impart some truth he can verify to show that she means them no harm.
She sits with her hands in her lap, waiting. Being a woman is not enough to save her. She slows down her breathing, tries not to blink. He will not torture her. She is a victim. She is innocent.