A sound basis for appeal only if their arguments were themselves legally sound.
And that’ the issue in a nut shell - no one out side of the eligibility crowd thinks that the natural born citizen = two citizen parents is a legally valid argument.
The Indiana Appeals Court affirmed that it is indeed legally valid. It was the ONLY question that it directly acknowledged was answered in Minor v. Happersett. Of course, they failed to understand that Minor also answered the question about the children of aliens and split parentage, by showing they could only become citizens through naturalization or Constitutional amendment.