Your ancestors did not have to “prove” anything when the census taker came to the door. They could get by just answering the questions and if the answers were totally wrong or just a “little off,” the census taker might not even know.
This does not mean that every census enumeration is wrong or that everyone lied on the census. But it does mean that an age that is slightly off or a birth place that isn’t quite right is not usually enough to throw an entire theory out the window.
But then again, there’s always that chance that great-great-grandma fudged the number of years married to make a few things fit–for those census records that asked that question.