Perhaps to clarify: the AI always play at the same level of intelligence.
Whether it gets bonuses or penalties depends on your setting (the difficulty level of the human).
That is why the difficulty setting for the AI civs are greyed out - it wouldn't change a thing.
And yes, this means you can't have one AI play at Warlord difficulty level while another is playing at Prince. They all get the same bonuses or penalties, so the only difference from their perspective is whether one Civ gets the same: namely yours, the human Civ.