[treading carefully so as not to offend]
I grew up in a Fundamentalist Christian church. And in my personal experience, when people say "saved," they mean something other than "being a Christian."
I can only speak for the church I grew up in, and for the ones like it that I knew . . . but the church in which I was raised believed that you had to have an experience in which God called to you, you made an open and public profession that you wanted to accept Jesus into your heart, you confessed your sins (not publicly), and you were therefore considered "saved." This usually occurred at the end of services, when we had the altar call. Altar calls happened at the end of every service I've ever attended at my church. I've even seen them at weddings and funerals.
As a child, probably around 7, 8, when I attended other church services (Methodist, Catholic), I saw that they did not do altar calls. I asked about this in Sunday School--the lack of the altar call. "Then they're not saved," my teacher said calmly. "And they won't go to heaven?" I asked. "No," my teacher said. "You can only go to heaven if you are saved."
I was mildly terrified by this for some time, as I'd gone to the Methodist and Catholic churches with my grandparents and aunt and uncle. Who were now, I learned with great fright, going to he11. (I later amended this belief, but religion's much simpler when you're 7.)
I'm not saying that the belief in being saved as a necessity for salvation is good or bad, wrong or right; that's not my reason for posting this. I'm posting because, having grown up in a church that did see a HUGE difference between being "Christian" and being "saved," I can imagine--not know, as I don't know this man, but imagine--what the man in the hospital meant when he asked. Being "Christian" is one thing. Being "saved" is another.
And since it is a tenet of the faith of many people who do believe in being saved, it is of the utmost importance that you work to make sure everyone else is saved too. You are failing as a Christian if you do not do everything within your power to try to make sure everyone with whom you come into contact is saved.
Again, I want to stress: I am not endorsing nor condemning what the man in the hospital was doing. I'm simply sharing anecdotal experience.