We could just use statistics.
Example: the DNA has 3.2*10^9 base pairs. We have trillions of cells. Even if each cell division introduced 1000 mutations, the cells would hit the Hayflick Limit at around 60 divisions. The last generation of a cell line would have 60000 mutations on average and the other cells less so.
It's nothing compared to the size of the DNA. I can't go through with the calculation right now but my guess is that it wouldn't take more than a billion cells to get to your birth DNA.
That part of my argument was just an easy way to deal with the writer's assumptions.