CTlawyer,
1. If military law applies on the base and even the postal address is a military address then how can it be said to be under the sovereignty of the country in which it is found? If it looks like a duck and quacks like a duck it must be a duck.
2. What standing could there be under restrictive American standards? Anyway, you can correct me if I am wrong but to the best of my knowledge there is no law that states that someone who is not a natural born citizen may not appear on the ballot. If he wins he cannot serve. Thus, it would appear that there can be no case unless Cruz wins the election in Nov. Even then, it would seem that the only one with standing to challenge his election would be his opponent. After the hue and cry over Bush v. Gore SCOTUS might very well not want to get involved.