Academy and world wonders survive--even in revolt.
Sounds like you didn't test yet either.
The information is valid and is supported by testing and XML-inspection, although it depends upon one's definition of the words "Cultural Building." Let's come up with a better term, that of "Buildings which cannot be Captured."
Shorter answer: Unless you have some City Culture in the City in which Moai Statues exist, which you get from ending a turn when owning a City in which you are earning Culture in the City, or from a Spy's Spread Culture Mission, you will have a 0% chance of retaining Moai Statues upon City capture. If you have enough City Culture in the captured City relative to the current owner of the City to be able to capture the City with 0 turns of City Revolt, you will keep Moai Statues (assuming that you don't have Moai Statues in another City). Otherwise, it's a dice roll chance of keeping Moai Statues upon City capture out of the percentage of the amount City Culture that you have in the City relative to the amount of City Culture that the current owner has in the City.
Longer answer:
Buildings which cannot be Captured:
A] Monument (assuming that you do not own Stonehenge, in which case it's not actually the Building surviving but a free fake Building appearing which will disappear upon losing Stonehenge or upon obsoleting Stonehenge)
B] Library
C] University
D] Theatre
E] Temple
F] Monastery
G] Cathedral
Note that this list includes Unique Buildings of the same type. Since a Monument cannot be captured, the Egyptian Obelisk, the Ethiopian Stele, and the Native American Totem Pole also cannot be captured.
All other Buildings have the potential to be captured.
Note that you can verify this info for yourself by looking in the XML:
{Civ 4 Installation}\Beyond the Sword\Assets\XML\BuildingsCIV4BuildingInfos.xml
In that file, a value of:
<bNeverCapture>1</bNeverCapture>
means that a Building cannot be captured. However, these Buildings will still survive a Culture Flip and will survive when a City is gifted. I assume that these Buildings will also survive when a City is assigned via The Apostolic Palace, but I don't have much experience with that case, so I cannot say with 100% certainty.
As for other types of Buildings, the percentage chance of a Building being captured is the combination of the <iConquestProb> value (found in the same XML file) and your City Culture percentage for the City, which, from what I can tell, only matters as the percentage of the amount of City Culture that you have in the City relative to the amount of City Culture that the current owner of the City has in the City, ignoring City Culture from other past owners of the City.
Culture is a bit tricky as there are both City Culture and plot Culture.
From my understanding of the two:
A] City Culture comes from you owning the City at the end of a turn and the City gaining Culture at the end of your turn
B] Plot Culture also accumulates when you earn City Culture, but it generally accumulates at a greater rate, since you get a bonus 20 plot Culture in the City Centre square at the end of each turn for every amount of Cultural Border expansions that your City has undergone. I.e. If you have a Monument and a Palace and are making 3 City Culture per turn, but your Cultural Borders have expanded twice due to you reaching 100 Culture on Normal Game Speed, you'll earn 3 City Culture and 3 + 2 * 20 = 3 + 40 = 43 plot Culture
C] In the Beyond the Sword expansion, a Great Artist Culture Bomb (aka a Great Work) that was bombed from another nearby City will not increase the City Culture of Cities within range of the Culture Bomb (although it will obviously increase the City Culture in the City in which you performed the Culture Bomb, as it's City Culture that is used for the Legendary City level that we attempt to achieve in 3 Cities in a Cultural Victory). Put another way: A Culture Bomb in BtS will not help you to reduce the amount of City Revolt upon City capture of nearby AI Cities that were affected by the Culture Bomb. This fact means that Culture Bombing in BtS does not help to increase the odds of capturing Buildings in nearby AI Cities. Although I haven't tested to be certain, I think that this behaviour was a change from Warlords and Vanilla, since Culture Bombs were much more powerful there, likely because Culture Bombs there affected both plot Culture and City Culture
D] In BtS, a Spy's Spread Culture Mission will affect City Culture (I'm not sure whether or not it also affects plot Culture). This fact means that the Spread Culture Mission is BtS' (likely, but not confirmed with testing) answer to the Vanilla/Warlords Culture Bomb, in that it will reduce the amount of City Revolt upon City capture
E] What we see when hovering our mouse over top of a City in the main game view and when looking at the City Nationality bar at the bottom left of the City screen is plot Culture
F] Below the City Nationality bar is a Culture bar, which indicates your City Culture in the City
G] Only the current owner of the City has their City Culture shown in the City screen, so you'll have to perform the math yourself in order to figure out the percentage of City Culture that you own in a given City, since the game doesn't display this information
Some general rules:
i. World Wonders have <iConquestProb>100</iConquestProb>, so they will survive a City Revolt
ii. Great-People-built Buildings, such as Academies, Holy Shrines, and Military Academies, have <iConquestProb>100</iConquestProb>, so they will survive a City Revolt
iii. Many Buildings have a <iConquestProb>0</iConquestProb> value, including Moai Statues, which means that if the City goes into City Revolt upon capture and you have no City Culture in the City, that Building will get destroyed
iv. Some Buildings have a value greater than 0 but less than 100, such as Granaries and Terraces with <iConquestProb>66</iConquestProb>, so if the City goes into City Revolt, the Building has a chance to survive
v. If the City does not go into City Revolt when the City gets captured, due to your Cultural dominance in terms of City Culture (plot Culture does not matter), all Buildings which are NOT in the "Buildings which cannot be Captured" list are eligible to survive
vi. If the City does go into City Revolt when a City gets captured, the percentage of the Building surviving can be greater than its <iConquestProb> value (up to a maximum of 100) if you have some City Culture in the City. The greater the amount of your City Culture in the City relative to the amount of the City Culture belonging to the current owner of the City (i.e. the current owner just before you captured the City), the greater the chance that Buildings with an <iConquestProb> below 100 will have of surviving. From my understanding, you'll be able to push Granaries/Terraces up to a 100% chance of survive, and other Buildings with a <iConquestProb> value of 0 will have a chance to survive based on a dice roll relative to your City Culture percentage (not plot Culture percentage) in the City
In testing, I have seen some interesting things:
a) Captured World Wonders that you did not build do not produce Culture for your Civ, which most of us know and makes sense, since the conqueror didn't actually erect the World Wonder. That's not the interesting part, but is the basis for why some other items are interesting
b) Most captured National Wonders that you did not build do produce Culture if they survive through the capturing of the City, but Moai Statues built by another player does not produce Culture for you, perhaps due to it being added in the Warlords expansion by a different programmer than were the original National Wonders. If you built Moai Statues and recapture it, you will get its Culture. Other than the Moai Statues exception, think of it as the National Wonder switching its national identity, but a World Wonder retaining its original national identity
c) Captured National Wonders that you did not build which retain their Culture (examples include the Heroic Epic, the National Epic, and the Globe Theatre) will retain their "doubled Culture" value if they have existed for 1000 years
d) Captured Castles that you did not build retain their +1 Culture
e) National Wonders can be captured regardless of whether you meet the pre-requisites for building those National Wonders. For example, I was able to capture the Globe Theatre with 0 Theatres in my empire, and the normal pre-requisite is 4 Theatres for Duel maps, then scaled up for map size, and set to 1 for a One-City Challenge game
-306gpt (when building no wealth)
maybe I can beat this city senseless and get it out (save it for another post)
)
. Yea, you missed a great bargain, but shouldn't stop you from BC space. This would be at least the 3rd time you stole my thunder, Kait 
