No, not correct. It's less of a debt and more of a duty, and less of an apology than an acknowledgement, and not a guilt but a recognition.

I didn't own slaves, I didn't commit genocide, and neither did my ancestors. But I benefit from slavery that did exist, and my ancestors benefited from a genocide. Do I owe anything to the victim? No, because the victims have been dead for decades if not a century. But a failure to recognize ones obligation or duty to the rest of their community to bring an equity about such that their children or grandchildren don't even consider such questions - that's not nearly at the scale of destruction as our history has wrought but it does continue the cycle. If you want future generations to break from it, it starts by reconciling that your status is derived from the status of those who came before you, and that's not necessarily a good thing.