Actually, no.
The foreign-born child is a citizen AT the moment of birth, not BY the act of that birth, at least not any more than it makes him/her a live human being, which is the requirement of any US citizen. My dog, born here, is not a citizen. Not enough chromosomes.
However that NBC status can be revoked if that NBC child fails to commit certain acts; residency, etc. or commits certain acts, renouncement, etc.
> The foreign-born child is a citizen AT the moment of birth
Not always.
For example, the Immigration and Nationality Act, Pub. L. No. 82-414 § 301(a)(7), 66 Stat. 163, 236 (1952), the foreign-born child is not a citizen if the citizen parent does not meet the requirements of this statute.