You are correct--in theory.
In practice, the NSA collectively view everyone outside of the Agency as foreigners and enemies. Therefore, due process of law even within the USA's borders means fuck-all to them. So in actually, Americans within the US have no more real protections than non-citizens, especially when you have pliant judges and magistrates who will sign on the dotted line cuz National Security.
In some rarefied Platonic universe, we all have natural, inalienable rights endowed us, but unless they are recognised, enforced, and vigilantly defended, they aren't worth the paper upon which they're enumerated.