Though I'm not familiar with this specific case, I can potentially shed light on it using a separate but I think analogous example: Egyptian King lists. Largely the reason we have all the names of various pharaohs in order is because of archaeological finds which document lists of ancient Egyptian Kings. However the interesting part about these king lists is that many of our surviving sources for the kings of the old kingdom (2700) of Egypt come from the new kingdom (1570-1544) more than a thousand years later. The new kingdom lists all seem to match up relatively well with cartouches on old kingdom sites and artefacts, with some mistakes and chaos especially in the fourth dynasty. So, how was this possible: non-surviving sources.

One of the biggest issues with studying any ancient society is the issue of sources not surviving to us in the modern period, these likely were a combination of written and oral sources. Herodotus, for instance, tells us that when he went to Egypt had a priest recite to him his lineage and genealogy going back to a God, is it likely then that there were also those that held geneologies for the pharaohs in an oral form. In addition there may be many other king lists that do not survive to us today, even the Palermo stone which records many kings of the old kingdom survives only in fragments. The Egyptians also wrote on papyrus which does not survive nearly as well as stone, though it still sometimes survives in Egypt anyway.

So long story short, I think that the situation of Sima Qian is a similar situation to the Egyptian King lists of the old kingdom which were written in the new kingdom with a comparable time gap. Sima Qian must have been working with older sources that we are not aware of as they do not survive to us today.