We had access to a church gym in each of my areas if we wanted it. All we would have to do is talk to the Ward Mission Leader or Bishop and they would gladly let us use it. Second thing, we were required to exercise for 30 minutes each day in the morning. There were some football players that served in my same area that would talk their companion into waking up even 30 minutes earlier or so to get a full hour or exercise in.
The point I am making is I could easily see how he could be an effective missionary who follows the rules AND shoot hoops every single day. No shame in admitting that.