No it doesn’t. It’s never been so.
I must respectfully disagree my FRiend. Natural born citizen is clearly a higher category of citizenship required to be president of the country, otherwise why would it have been specified as such in the constitution? As understood at the time of the founding, natural born meant the issue of citizen parents who would have no divided loyalties. Conflating native born with natural born does not make sense because that would make US-born children of illegal aliens eligible for the presidency.
This issue really cries out for a definitive SCOTUS ruling but unfortunately it is always too hot to touch or too cold to be of interest to them.