I do believe fear was a major factor in a Confederate veteran not revealing his past, especially Tennessee. Governor Brownlow put the fear into them.
There are others too.
Many old Southerners also didn't like the census takers and wouldn't give them a straight answer.
Many old Southerners didn't like taking what was deemed charity or hand-outs and would not take the pensions, and didn't want their names on such a list.
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David Upton