Okay, I started looking into this. My initial assumptions turned out to be correct. The decision to convert significant culture to the new owner whenever a city is conquered has basically ruined how city conquest works otherwise, especially when recapturing cities. Because the base rules already have exemptions in place when recapturing one of your cities, in which case the city loses neither population nor buildings. However, the game uses city culture to determine if you are the legitimate owner recapturing the city, i.e. you still need to have the most culture in the city for it to count as reconquest. This is generally a good rule in my opinion because it naturally stops applying over time as the new owner adds their own culture, but with the culture conversion rule it immediately stops applying because usually the new owner already has majority culture.
Over time this might actually have a significant impact on areas where cities change hands more often. I considered whether I should change this rule but it's quite simple and elegant and it's hard to come up with something better. So instead I will replace culture conversion entirely, and come up with a better solution to enable control over some recently conquered territories.
By the way, this is also why culture garrisons are much less important in DoC than usual because the amount of garrison units required to keep a city pacified also depends on the culture differential.