At the research company where I work, there are three parallel career tracks: scientist, engineer, and manager. Manager is obviously quite different than the other two, and eventually ends up with the person doing little or no technical work. The only distinction between the scientists and the engineers, however, is determined post doc by observing what the person tends to do: scientists are the people who tend to publish a lot and lead research projects, and engineers are the people who don't do those things much.
Science is not a tribe, nor is it a credential, nor an award. Science is a behavior: performing investigations that contribute to human knowledge. Any person who does this, I would call a scientist, in addition to whatever other labels may be appropriate.
In the case of your example, Ben Carson, a quick Google Scholar search shows he's got a lot of publications, many well-cited (easily 2000+ citations, H-index of around 35). Even without reading any of it to see if his work is ultimately borne out or refuted, it is clear that this is a person who has make a significant intellectual mark on the scientific discussion of their field. This is not surprising: careful and well-presented clinical reports are an important contribution to knowledge! Complementarily, a non-scientifically inclined doctor might simply treat their patients and not write the cases up for publication, merely keeping their private records in accordance with normal medical practice.
In short: definitely a scientist, no matter what else he may or may not be as well.