She'd contest the "vital" part, but she did leave her story deliberately vague. She has no way of knowing if these two Jims have similar timelines and if she could cause an issue mentioning something to one that only applies to the other. Best to say only what's necessary right now.

His question earns a single huffed laugh. "The better way of phrasing it is that he often dances around the truth. There are many things he doesn't want to talk about, as I'm sure you don't either, and given our history? Neither of us is eager to give the other more fuel to add to the fire." Another polite deflection of how much she hates the other Jim Kirk knowing about her and how she used to be with everyone. But at least this one is closer to the whole truth.

As she turns back to look at him, she tilts her head a little in question. "Can I ask that you be more straightforward with me? In return, I offer to be the same." Maybe she can't fully repair the relationship she has with the first Jim Kirk she met, but she can at least try harder with this one to start.