I don't know what that person meant but, like many in the region, Koreans have family registries (戶籍) that record their family lineage. At least among people I've known who have spoken about theirs, Korean family registry records tend to go back much further than the median east Asian country.

The names of the systems related to this registry are slightly different in Chinese, Japanese and Korean but you can see links to Wikipedia entries for each of them from here: https://en.wikipedia.org/wiki/%E6%88%B6%E7%B1%8D