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.
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“the census taker might not even know.” – or the opposite could be true ('the census taker might know') when one considers the fact that the Census Bureau has generally hired enumerators who live in the enumeration district. It's a 50/50 chance, isn't it…
I'm not certain it's 50/50, but it is plausible that the census taker did know some of the information–or worse yet, thought he knew and wasn't right. Census takers in rural areas, probably knew the names of a great number of the enumerees and probably some relationships, but ages and places of birth are more problematic.
One can easily give the wrong information when in a hurry or distracted. While signing up for a web site with user name, etc. and those questions like your favorite car, or father's middle name I gave my father's first name!! I knew better, but just got in a hurry.