Yep. When you take over an enemy city, all culture buildings are destroyed and all the culture generated by wonders is set to zero.
in warlords, if the other civ's version of your unique building survives when you capture a city, it turns into yours.
granaries very often stay when a city is captured. they're not culture buildings. the incan UB is the terrace, a granary with +2 culture. terrace is coded as buildingclass_granary and not a culture building. the end result is that huayna can and often does capture cities with granaries that turn into terraces, which act culture buildings as soon as the cities comes out of revolt. that part i know is true, you can quote me. if anyone else captures his terraces, of course they revert back to ordinary granaries if they don't get destroyed.
don't quote me on this part, it's purely memory ... but i think that they double as the game goes on, even if someone ELSE owned them during the early years. so that if huayna captures a granary very late that was built very early on, the terrace if it stays might be worth +4 culture per turn when he gets it.
the first part, about how the building being a granary not classified as a culture building, i can't see as a bug really. if they want to keep his UB the way that it is, it wouldn't be fair to not let him keep granaries if everybody else gets to keep them, and it would suck to not let anybody keep them.
but if the game somehow calculates culture for terraces as double over time (i'm going by memory here, haven't checked saves to verify), then it seems awfully fishy that huayna would get the benefit of it doubling due to someone else having built it ages ago rather than yesterday. that can't happen with any other buildings
by design, since culture buildings can't be captured that way. i can't justify that one in my head (altho i'm not saying i mind it when i'm playing HC myself).
just a captured-culture quirk.