If I was falsely accused then that would be my defense...
You missed the point of the analogy, which is a defense of why lawyers must be amoral actors. If lawyers are moral actors, then if your defense attorney is convinced by the prosecution that you were not falsely accused, but actually guilty, then he is morally obligated to offer no defense. In the best case, he recuses himself, leaving you without an advocate, but in the worst, he rests, without presenting any defense at all, leaving you at the mercy of a judge or jury who has/have only heard one side of the case. If your defense attorney is an amoral actor, though, then he is obligated to present the most effective defense that he can, whether he's convinced that you've committed a crime or not. Maybe that is a presentation of the truth of the case, that you were falsely accused, or maybe that's digging up some obscure legal verbiage that indicates that the action you were accused of was not a crime at all.
This does lead to scenarios where defense attorneys have to put up a vigorous defense of someone who is clearly guilty, occasionally ensuring that a monster will be acquitted of his crimes and turned loose on society again. Lawyers don't do this because they are moustache-twirling villians who want society to burn as a sacrifice to their salary. They vigorously defend the guilty and innocent alike, because it is an essential function of our justice system that minimizes the number of innocent people victimized by false accusations or misleading evidence.
It's not a perfect system, but it's vastly preferable to one where lawyers, as moral actors, can and must opt out of your defense, when they become convinced (rightly or wrongly) of your guilt.