Again, this is not my forte, but your post doesn't make sense to me.
In the first part you say that becoming a citizen of another country isn't relevant, that becoming a citizen of another country would have no effect on their US citizenship.
Then you say that only having US citizenship at birth, according to the law (which depends on the parent's residence in the US and marital status) and whether they renounced or intended to give up US citizenship, matter.
The part that's confusing is, if becoming a citizen of another country doesn't have any effect on your US citizenship, how does renouncing your US citizenship matter? You would only renounce your citizenship if you become a citizen elsewhere, which, according to you, doesn't matter in the US. You'd still be a US citizen. Or am I misunderstanding what you're posting?
The two seem to contradict each other.

