The best brain surgeon in the world may be an obese, physical wreck. For example, watch newscasts where a group of doctors is announcing a new medical breakthrough and look at the physical condition of the doctors standing in the background. Conversely, a sports superstar with a rock hard body may be an illiterate idiot. For example, watch interviews with sport stars.
For this discussion of SMEs, let us use the example of a trainer and a boxer. Some SMEs require mental prowess, such as a trainer who trains a professional boxer to fight, while some SMEs require physical prowess, such as a professional boxer who fights in the ring. A trainer only needs minimal physical prowess, and a boxer only needs minimal mental prowess. Both the trainer and boxer may argue this, but the bottom line is that—it is true. Both trainer and boxer may have a lot of physical and mental prowess, but a lot of both are not required for each to be a SME.
Although the trainer may be, or may have been, an outstanding boxer; it is not required for the task. The trainer does not need to be able to physically box; a trainer develops strategies for the boxer. A trainer only needs to be able to obtain the best performance from a boxer; this requires much mental prowess and little physical prowess.
A boxer needs to be able to box in the ring, but this requires little mental prowess. The trainer develops the strategies needed to win, the boxer only needs to carry out the tactics, to punch hard and hit the target, which requires much physical prowess but little mental prowess.