Best do flapping wildly, because that explanation is I am afraid boll*cks. It ignores the fact that though there may be more surface behind teh widest points, the pressure is more lateral in direction. Overall they pressure all cancels out if you consider vectors - until the fish starts swimming of course
p.s. if you do not believe me, put something fish shaped (or triangular) in still water. Does it move in the direction of the widest end?
(The answer will be no)