I think those who played in a 'roleplay / pretend to be a civilisation leader way' or what ever you wish to call it we were aware that the historical veneer was thin and the link tenuous. It was enough however.I mean to be fair, the premise of "Building a Civilization that passes the test of time" was always a fiction. Basically no ascendant civilization in its modern incarnation has passed the test of time (except maybe China? disputable depending on how much you think there's continuity between dynasties) and has morphed in such extreme ways as to be unrecognizeable to those who inhabited it a thousand years ago in borders, language, government system, etc.
I do wish leaders were tied to Civs per era and you got a new leader for each era you progressed in, but I feel that if one is talking about connections to history one is hopelessly deluding themselves with the idea that prior Civ games were historical without mods. Seeing Abraham Lincoln wearing a sheepskin hat and coat in Civ 3 was never historical, even if it was endearing and funny; neither was Joan of Arc persisting into the modern-day as a football hooligan. Civ 4 just straight up does away with era progression for leaders and just pretends the leader is existing in a historical vacuum from the civilization they're leading, which while less distracting is no less ahistorical.
Certainly playing tsl maps, or specific scenarios helped a bit with that as well.