Absolutely correct, although I suspect the luminaries on the Supreme Court may disagree with you, and they appear to be the final arbiters of Constitutional questions. Sections 2-5 of the Fourteenth Amendment use the word "shall," imposing a future obligation upon the government. The first sentence of section 1 uses "all persons [...] are citizens," which rectifies the injust conditions that existed when it was ratified, but does not impose any future or standing obligation upon the government. An originalist, literalist, strict constructionalist, whatever would not find any support for granting citizenship to "anchor babies" in this amendment.
When families of diplomats living in the US have children here are those children automatically US citizens too?