It may be fun to sketch out far-flung scenarios to explain that census enumeration or birth certificate that does not make sense. But remember that reality is often more mundane than the fiction we create in our mind and often the simplest explanation, or something close to it, is likely what actually transpired.
It can be helpful to think about possible scenarios when trying to determine what records to search next, where the family might have been from, etc. but focus on the situations that are most reasonable–unless the records indicate something more atypical was taking place.
You should not have to violate the laws of common sense, physics, and biology for a scenario to have played out. Violating state law could easily have happened–fortunately records may have been generated.
Keep the explanation as simple as possible–at least until you locate actual records that are consistent with a more dramatic reality.