Weight training without flexibility is not the answer. Ideally, you should have both. But the trophy rooms of PGA TOUR venues across America are filled with pictures of scrawny little fellows hoisting big silver cups above their heads. By all means build up the strength in your legs and your forearms. But be careful about building up strength in your torso and shoulder areas at the expense of flexibility.
Fitness is fine, and flatbellies definitely have the edge in the modern game.
But fitness without freedom of movement doesn't do you much good. Most golfers fancy themselves at some level as athletes. Many grew up playing sports such as football, baseball or basketball. Almost all athletes are taught to aggressively use the strength in their upper body. The small muscles must re act to the motion of the big muscles.