If we are looking at the system from "above", like looking down on a plate on which peas are rolling around, then the apparent distance between them is the same as the actual distance between them. If we're looking at them edge-on, then we don't really know how far apart they are. The apparent distance sets the lower bound for the actual distance, but the upper bound is unknown. And yes, there's always a degree of conjecture in astronnomy. All we can really say is that there are three black holes near the centre of that galaxy, and they are almost certainly in orbit around each other.
What people don't seem to understand is, science relies on publishing of un-proven theories. You observe, model, predict, publish, and eventually you will be either proven right or wrong. Without the "publish" step, especially in long-term sciences like astronomy where it could take centuries for a theory to tested (such as, "will that comet return in a hundred years"), you could make a thousand contradictory predictions and then publish the one that happened - by co-incidence - to be correct. If you limit yourself to a single prediction, which turns out to be correct, then you are worth paying attention to. My mum is always saying "Scientists keep getting things wrong, therefore all science is rubbish". Getting things wrong is crucual to scientific progress.