People who talk about their genetic heritage are stupid
Even if you are a descendant of Shakespeare, there is only a negligible chance of your having any of his DNA. This is because autosomal DNA gets passed on randomly. Shakespeare's kid probably had 50 percent of his DNA; his kid in turn, on average, a quarter, and so on. Within 10 generations, Shakespeare's DNA has spread out and recombined so many times that it doesn't even really make sense to speak of a match.
Almost all humans have the same set of genes. Nevertheless, different populations have varying frequency and prevalence of gene expressions. For example, genes related to dark hair are present in Asian populations-including native Americans-but also in European populations. Ancestry reports just counts the prevalence of gene expressions and put people into groups like white, black, etc. It doesn't go back more than 3000 years. A person who calls herself an Italian today might have called herself a Gaul a couple thousand years ago and gone to war against the Romans. In other words, to divide people into groups, researchers make decisions: For example, they'll say, the members of this group of people have all lived in Morocco for at least several generations, so we'll add their DNA to the reference libraries for Moroccans. And people who had one grandparent with that sort of DNA will hear that they're 25 percent Moroccan. But that boundary, is fundamentally imaginary. It's not really science so much as it's description. If they were to be completely honest, what they should tell you is not that you're 47 percent Italian but that you're 47 plus or minus some error range …
Putting the same point the other way, each of us has so many ancestors that we have no choice but to share them with each other. Moreover, we don't share any DNA with the vast majority of them. True, you will share Y-chromosome DNA or mtDNA with very distant ancestors, but these make up a vanishingly small percentage of your total ancestry.