Yeah, the stuff I wrote in post #3 looks a bit abstract, better have some screen shots

-I now hope it's sure as eggs is eggs.
(klar wie Kloßbrühe...)
Anyways, the pic has another interesting problem in it: you
could e.g. grab that cow tile 2 tiles SE of New London with (e.g.) the next border expansion of New Varna, as long as New London's culture is below 10.
Now the problem (though we cannot see it in the right bottom corner, we know there is one of your cities as well):
Who gets the cow tile, if
-New Varna's border had expanded (so cow *theoretically* grabbed)
and its local culture is better than New London's
-New London had 1 border expansion
-'unknown' city in right bottom had no expansion
Cow *should* go to New London in that case, I think.
But total culture (ratio) won't matter. I once made a test scenario with heavily modded cpt rates of certain improvements (for different testing purposes, though). At some point, total culture ratio was like 1:gazillion, but there was no 'unusual' border behaviour. It was always local culture (respectively rules posted above) that determined borders.
Btw, there's another update problem (it's actually a minor bug): Sometimes (e.g. if you get a city through peace treaty), even if the borders are updated correctly, the working tiles' ownership is not: citizens from a rival neighbouring city could work tiles within your borders! There was even a SOTD about it IIRC. The problem normally vanishes in the next turn (maybe as well by 'leave or declare' option, if present).