Well, if a local citizen mother gave birth on a US base, would the child be a US citizen? I really doubt it.
The claim was that overseas US military bases are US soil. I said that I don’t believe that is true, the US does not have sovereignty there. The same thing is often said about embassies, that they are actually the sovereign soil of the visiting country. That’s wrong, too.
The last part is the sticky part, “subject to the jurisdiction thereof.” Though the SCOTUS has ruled as the OP stated there is nothing to prevent them from changing their minds. Since diplomats are not subject to US jurisdiction their kids aren’t citizens but I have seen many attempts to “prove” tourists aren’t really subject to “all” jurisdictions. Indeed the SCOTUS has ruled tourists have the same “basic” rights as US citizens but not “ALL” the rights of US citizens