Why does that not make sense? We evolved from single-cell eukaryotic organisms and while maybe not an exact copy at this point there surely is evidence that our current version of some genees are derived from the single-cell ancestor's version with a similar structure and function.
I'm thinking in terms of provable ancestry. That you could exhume the body of a presumed distant ancestor, sequence that DNA, and prove that was someone's ancestor. It can't be done if the ancestor is too many generations distant. If it can't be done, would be it be accurate to say that the descendant carries the ancestor's genes? I don't think so.