He understood all too well that just because someone wasn't carrying what looked like a weapon didn't mean they were unarmed. There were people who had powers that were simply a part of them and there might be technology he simply couldn't see for whatever reason. He wasn't inclined to underestimate her just because she didn't have a traditional gun strapped to her hip. The little trick with her aim didn't go completely unnoticed. He was trying to guess a little at what was different about her without letting himself get caught up in his thoughts.
"I wouldn't betray your confidence without reason but if you are dangerous or sharing this information would protect people, I would be obligated to do that," he informed her, making a point of looking her in the eye. "Do you understand? I'm not going to go spouting off at the mouth or running to the police like a lackey but I am invested in this place and I want it to be safe. I'm hoping we're in agreement on that point. If not, I understand if you won't show me, and I hope we can part ways peacefully."
"But really, I hope you understand where I stand and that you'll show me anyway." Because he had his principles and he wasn't going to hide them. He wouldn't blindly swear to keep a secret forever just on threat of force. He would only reveal it if absolutely necessary, to protect others, that was all.