Nothing is more embarrassing than being disqualified. Better to come in second than to come in first only to be disqualified. Nothing carries the stigma of dishonesty, or lack of integrity more than having the appearance of winning, only to be discovered at the end of the race and humiliated with disqualification.
How people become disqualified is directly tied to this word, integrity. It's lack of integrity during the running of the race that leads to disqualification. Or, in Paul's other image, it's lack of integrity behind the scenes, during the training process - like that boxer working out in the gym - that fails to equip and empower the athlete for the battle ahead. And there's no doubt about what Paul's after in that illustration - the desire to win without work - to look good in front of the crowd without paying the price in the hours alone in preparation.
And all of that relates to this subject of integrity.