Seems like I saw somewhere that the Nazis were experimenting with the end-goal of anti-gravity during the late war period and that the reports filed by the guys in charge were promising but the war ended before the work could be completed.
Now, given that we are not enjoying the fruits of Anti-gravity technology, today, seventy years later, suggests to me that either the whole thing was a misunderstanding and nothing of the sort ever existed, or that some scientists may have been blowing smoke up Hitler's skirt to keep the funding going for a pretend science project.
But, in Star Trek's timeline, maybe they did strike onto the right idea, but nobody could quite figure out the specifics of how to make it go before much later. Or, maybe the technology was more or less nailed down by the late 60's or early 70's and was kept secret for a while while the powers that were had a go at weaponizing it. Perhaps the ability to make gravity is easier to figure out than to cancel gravity and therefore it was being used in space applications but not much need for it on the ground in everyday roles (being as how Earth makes enough gravity by itself for most people's needs). I have no qualms with the origins of AG tech on Earth as shown in the various shows. I don't see any contradiction there at all.
Since we are clearly dealing with an alternate timeline and tech progression, I would say that it is very possible that some form of AG could have been experimented with and varying degrees of success or failure recorded. Something must said about these obscure sources making claims, and it makes for mighty-fine storytelling.