Is it possible for an neighbor's apartment to have mice but not mine?

I just found out that my neighbor that I share a wall with is moving out because of "the mouse issue." This is the first I've heard about it. I'm pretty sure I don't have mice. I haven't found any chewed food packaging or what looks like mouse droppings. I do have a cat but I'm not confident he would know how to kill a mouse. I've never seen him chase anything on the floor but I know he will chase flying insects. I also haven't been presented with any "presents." Could he really be keeping the mice from my apartment by just his scent?