Methinks this couple are surrogates of an effort to overturn the law; how, for instance, did the city come to know their marital status and the parentage of the children themselves?
That's a good point. From my reading, I would guess that the city found out about it on their application for the permit. Also, a Board of Adjustments hearing is the first step towards taking it to court.
Personally, I hope they take the city for all they can get. Discriminatory practices put in place by a few church ladies who want to use building codes to stick their noses into other people's business isn't how any government should be running things.