If AI 1 takes a city from AI 2 on your boarders it can still flip to you, no matter what the setting above ist. "No Culture Flipping After Conquest" only prevent flipping back to the previous owner (To any of the previous owners, if the city changed hands more than once.)
Also if you use NO culture flipping after conquest a couple of oddities occur - the game does not check if the city was ever conquered - it only checks if it was ever owned by someone - then a city can never flip back to someone who owned it in the past. Meaning that you can not flip back cities in a culture war, or theose that have been reassigned by the AP.
Hence i play with "Culture Flipping after Conquest" enabled, because i don't want to restrict the strategic possibilities. But i dont concider myself a hardcore warmonger.