The case were denied on standing not merits of the evidence. Only Congress can remove obama, not the court system.
Point being, the court won't hear them because they don't want to. They'll all find a reason -- and "standing" is convenient.
What you are calling "evidence", if it applies to the NBC theory, isn't evidence at all. It's an opinion of what you (and Vattel, et al) think the constitution means.
There are other opinions that are equally valid.
Only Congress can remove obama, not the court system.
And Congress won't do it, either.