Not quite: the USCIS rule being referenced (https://www.uscis.gov/archive/uscis-implements-new-law-related-to-citizenship-for-children-of-military-members-and-us-government) doesn't have anything to do with being born on a military base, and basically just removes the residency requirements for deployed military/government workers. For example: the parent doesn't have to be living on the base, the kid can be born in a local off-base hospital, etc... and they still get citizenship (as long as you remember to file the paperwork). It doesn't matter so much *where exactly* you're born, so much as who your parents are and why they're there.
In other words: Military bases overseas are still not considered US soil for citizenship purposes. Otherwise, a non-citizen working a civilian job at the base that happens to give birth there would give birth to a US Citizen. And yet, no law or regulation I'm aware of makes this the case