Was never in the military but I'd guess it's a combination. A Seal (or any elite military group) must be very strong willed and physically fit to do their job.
75% mental 25% physical. Look at any of the Spec-Ops. In training they first have to mentally break you before they can build you into the soldier capable of handling the mission. It is easy to make a body physically stronger but very difficult to achieve mental break throughs.