I missed (or misread) "inception" in your earlier post. Your statement does allow for the introduction of novel genetic variations.
However, your description of the methodology of cladistics is only partially right and (I think) the origin of our disagreement. accepted cladistic classification philosophy (which Ancesry depends upon) assumes that individual genetic variations enter the population once and pass down the specific hereditary branch from that particular instance is only true if a more parsimonious cladogram can not be constructed from the same data set. Parsimony is the only criteria for cladistics (which is where its greatest criticism originates...garbage in, garbage out). It does not disallow the possibility of identical genetic variation originating in extant and separate evolutionary lineages if it constructs a tree with the smallest number of steps. Of course, this becomes highly improbable, as the number of identical variations increase.