Muscle helps if you surf hard... a "power surfer." If you're a cruisy styler, not so much. But without the cardio to go along with it, you get winded faster... more muscle, more oxygen you need to feed those working muscles. So you need to do the resistance training AND the cardio to be able to maximize the benefit of the added muscle.
The third component in the trifecta is flexibility. Flexibility helps prevent injury (though not as much as some people might lead you to believe), but even more, it will help you recover from a lot of moves that you might otherwise just fall... think about those extreme laid back landings and tail slides. And flexibility training requires effort... not just laying in front of the tv and doing a couple toe touches. I'm talking a good half hour of yoga type stretching at a shot.
So an effective fitness routine should combine all three... resistance (strength) training, cardio, and flexibility. I do three days a week in the gym, combining cardio and resistance, and the in-between days I try to stretch.