Alice speaks the truth. There are a certain subset of deaths which fall under his domain. They have so many regrets and fear in their last moments. Her question is hardly personal when it relates to his job. Even if it was, he can tell this means something to Alice, and so he would have been more likely to answer.

"If they don't see me, then they see either Lord Hermes or my brother, Charon." He does not collect everyone. He wouldn't be able to keep up. He already couldn't keep up with his case load with their help. "But for those who fall under my responsibility, they do. I'm often mistaken for Lord Hades or Lord Ares, but I am the one who approaches them."