It’s mostly true; however, if a hypothetical Martian ambassador and his very pregnant wifeling were to visit the United States and have a child in Oakland, that child would not be a US citizen because of the qualification in the 14th Amendment, “subject to the jurisdiction.” The US extends exemption from our jurisdiction to the families of accredited diplomats and heads of state.
The other exception would be a Martian child born during an invasion of Oakland. Children of alien (pun intended) invaders born in occupied areas of the United States where the government is unable to exercise jurisdiction are also excluded from citizenship.
The Supreme Court explained the jurisdiction clause in the case of United States v. Wong Kim Ark (1898) saying:
The real object of the fourteenth amendment of the constitution, in qualifying the words ‘all persons born in the United States’ by the addition ‘and subject to the jurisdiction thereof,’ would appear to have been to exclude, by the fewest and fittest words (besides children of members of the Indian tribes, standing in a peculiar relation to the national government, unknown to the common law), the two classes of cases,—children born of alien enemies in hostile occupation, and children of diplomatic representatives of a foreign state,—both of which, as has already been shown, by the law of England and by our own law, from the time of the first settlement of the English colonies in America, had been recognized exceptions to the fundamental rule of citizenship by birth within the country.
But otherwise, the children of aliens (both non-citizen earthlings and humanoids from outer space) born in the US are natural born US citizens.
That “fundamental rule of citizenship by birth within the country” is called “birthright citizenship” and there are those who are against it, strongly against it. And there are those who make persuasive-sounding legal arguments denying it, persuasive unless you know the background, the cases and the authorities they won’t tell you about.
The US Supreme Court settled the question in 1898 when it said that a son born to Chinese immigrants (not US citizens) was a US citizen. Kamala Harris, born just across San Francisco bay from that man is a US citizen too.