While great-grandma could only have been born in one place, don’t ignore those places that are clearly incorrect. Sometimes wrong locations as places of events are out and out lies, but more often, they are clues as to where the people had lived at some point in their lives–just not the moment the person in question was born.
My great-grandmother has three different states of birth listed for her depending upon what record is being looked at. Every location that’s “wrong” is somewhere the family lived in the early 1870s around the time that she was born.
They moved a lot.
And people sometimes get “where you were born” mixed up with “where you were from” or where someone was living.