Just my 2 cents: many of these doctors have been trained in science, but I would not consider them scientists. Many of them have not participated in research of any kind (even the specialists). An MD is technically a bachelor's degree, where a contribution of original research is not required.
So, I would say, having a curious nature is not required and probably not an impetus for a person to enter med school. Of course, as we all know, there are many specialists who love to initiate and participate and follow research and are immensely curious and open to new theories. I love those people!