Can't raze a captured city in Civilization 4
From recollection1, you cannot raze a city in Civilization 4 if:
- City razing is turned off as a game option
- Your team's culture makes up more than 25%2 of total culture in the city
Short answer, but that's it. Note that you can still "disband" cities acquired through cultural flips.
[1] Later confirmed via acquireCity() and canRaze() in CvPlayer.cpp
[2] RAZING_CULTURAL_PERCENT_THRESHOLD in GlobalDefines.xml