Just out of curiosity, were those residents American graduates, or people who trained abroad? At least in my experience, only residents who attended medical school in India and the like tend to harp on these things.
On the very first day of my first rotation as an MS3, I initially addressed my intern and resident as "Dr." and was told that was completely unnecessary and that I never needed to do that again. That said, virtually all of the residents our university hospital were American MDs. As a resident, I've rotated through hospitals with more IMG residents, and from what I've seen, they're the ones who have their students calling them "Dr." and introducing themselves to me as "Dr." as well. Perhaps hospital culture is just more formal in Asia? Who knows?