How far back do we go?

There is a National Georgraphic project out there called the Genographic Project that traces back our DNA to see where we came from. As you can see from the site it says we all started in Africa. My question about how far back do we go relates to meeting people and their expression of their background.

Now I'm the first one to tell you that I am of Greek descent and not that I have proof but I would say that Alexander the Great was in my family tree (don't get me started on the Greek / Macedonian thing) but I think we pick a group of people we want to be associated with and make sure we can justify it. In some cases it's easy. Parents were from a Cornico so you have ancestors from there that go back a few generations and presto you are Cornicopian. For the last century the Cornicopians have been a bad bunch doing evil deads around the world or maybe they have been given a bad name by some questionable press so you want to disassociate yourself from them. You go back a few years before the Cornico Empire and call yourself a Precornis. Ah, those were the days, the Precornis were such a nice bunch, philanthropic, masters of art and medicine.
Is this allowed? How far back can I go or do I wait for the Cornicopians to make a comeback on the good side and refer to myself a Cornicopian again?

I'm not saying we should give up our culture or not look at the past but does it really matter where you are from or does it matter where you are today and why are you there? Oh yes we can use the past to prevent mistakes in the future but I don't see many people at an individual level doing this. Use of things like the Genographic project for benefits in health or advancement of science is great. Our background is important as there are ties to what we are and how we became who we are but lets not use this to claim we are better than others due to our ancestry. Maybe we have to prove our worth today so that future generations will want to call themselves decendents of Canadians or maybe we just say we are all the same as the Genographic project is concluding and work towards making everyone better.