Yes, you CAN refuse a offer of a city from an AI, but if a city flips to you, from being Barbarian, you CAN'T refuse it. It happened to me in my current game.
A Barbarian city, 1 tile CLEAR of my culture to its culture, suddenly flipped to me. I've NEVER fought a battle near it, NEVER had a city near it, as was in ice/tundra.
BANG suddenly its joined my empire, no chance to refuse/raise.
Solution - Never garrison the city, moved out the 'free' garrison from revolts and just waited till the near by Barbarian city, FINALLY sent a trooper to raise the city.
2nd instance. I captured a Barbarian city, proceeded to raise it down to ZERO population, no problem so far.
BUT at ZERO population, it wouldn't destroy, wouldn't raise below there, (so that's fixed

)
Again, I set to zero growth, no garrison, and just waited to EVENTUALLY a Barbarian rebel, from the AI city above it on the Island, took and raised the city, SVN 1047 for zero population, SVN 1049 for raising of city.
Note SVN versions are latest and version prior to 45's updates, so add/subtract to get correct version.