I've seen claims like this even in my own family. And it depends on what you mean by "trace." For instance, I can trace my father's family, names, dates, and proof of direct lineage back to the mid 1700s, Before that, I can find plenty of names mentioned in ship records or land transactions that sound like they are related. And I've read books that claim an "ancestor" was mentioned in this important document or that one down through centuries. But there is no direct linking of my earliest provable ancestor to those other names.
I guess it would be provable through related DNA testing, though.