If his father didn’t tell them that he was already married, the court wouldn’t know it. And where exactly were his parents ‘married’ anyway?
To the best of my knowledge, because both parties are deceased, Zippo would have to present a compelling reason to the court to change the ruling.
The only compelling reason he could present for the necessity to be declared a NBC instead of just plain citizen would be so he could run for president.
He would have had to change it before he ran for president and have a court declare him a NBC so he would be eligible to run for president.