Well, why shouldn't she believe him? From what she can gather, Byrne stands very little to gain by lying to her about this. And anyway, in her timeline at least, he's already more than proven himself trustworthy. The difference between this Byrne here and the Byrne she knows... is only a matter of time.

To his question, her grin turns rather wry.

"Oh, well, I'm not sure I should say! I wouldn't want to spoil the ending for you." She lets that hang in the air long enough to juuuust border on cruel, then continues. "I suppose I can at least say he was successfully defeated."