You are probably right. “and subject to the laws thereof” is the phrase in the 14th Amendment.
The law would offer the definition that children without at least one US citizen parent would not be subject to US law when their parents returned to their home of citizenship, and so such a child born in the US would not be eligible for birthright citizenship.
The law could, (note I do not say ‘should’) even make the same definition for children without two US citizen parents.
Currently in Title 18 of the US code there is a provision that children whose parentage is unknown and who is raised in the US from prior to the age of 5 years is be awarded US citizenship.
The best way to look at this is to consider who is excluded. Those born in the US who are NOT subject to its jurisdiction are a fairly precisely defined group. This group, according to common law, includes primarily foreign diplomats, essentially those with official diplomatic immunity, and armed foreign invaders.
Members of these groups are not subject to the laws of the US and thus children born to them on US soil are not citizens.
Everybody else, who are subject to US jurisdiction while on US soil, is eligible.
I seriously doubt the Congress and the States intended the legalization of anchor babies when they passed the amendment, but that is what it says.
Any other interpretation, IMO, requires ignoring the plain meaning of the words, similar to the way gun control people try to ignore the plain meaning of the 2nd Amendment.