Oh, he wouldn't fault them at all for using his expertise on that matter. It was the near-sightedness that this was all he was good for that amused him. All in all, it was probably a blessing. The less they knew about him, the better.
In that same vein, he felt he needed to spell it out for her as she put the onus of his noncompliance, and the consequences thereof, onto his head.
"Yes," he agreed, voice low. "If you come here, people will die. I can try to protect you, but we both know the percentages. I'll even the odds better than you can predict, but your people will die, and so will Gotham's. You would serve both of us best if you left before you have to stark asking yourself if it's worth it. Few outside of Gotham think she is."
Turning to face her, Batman came closer, stepping out of the shadows. He was visible now - or at least the mask was. "You fight for the world, Agent Hill. Gotham may be in that world, but to really defend her, you have to watch closely; look carefully. I don't expect you to do that - your view is wider - but don't come here, to my city, and tell me how it's going to be done, and who's fault it's going to be. Because it may not concern you greatly if a decaying city like ours falls as long as the world is still standing, but she is my home, and as long as there is breath in my body, I will fight to defend her. To the last stone."
He was toe to toe with her, angry, but his voice was mysteriously even, if intense. "And as for my name - the people I fight here are the worst kinds of villainy. Psychopaths, murderers, and any other kind of criminal you can think of. There are very few of them who wouldn't use everything and everyone I have against me." He took a few slow steps backward, never looking away. "Frankly, I don't trust that SHIELD wouldn't do the same someday. Just in different ways.
"You don't get my name," he said. "Get out of my bed."