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Notes -
People often mean very different things when they say "most common ancestor".
Do you mean the person such that every single person living today has as an ancestor somewhere in their family tree? This person is a mere 3,000 years ago: http://www.stat.yale.edu/~jtc5/papers/CommonAncestors/NatureAncestorsPressRelease.html
Do you mean the time from which every person living back then was an ancestor to everyone living today. That's about 7,000 years as you mentioned.
Do you mean the person from which a certain locus in all modern living humans descends from? This person is about 50,000 years ago (this is highly dependent on the locus though)
Do you mean the person from which all of a large block of the DNA of all living people comes from? This person is about 300,000 years ago (see e.g. Y-chromosomal Adam, the guy who all modern extant Y-chromosomes are descended from) and isn't even an anatomically modern human.
Do you mean the person from which all of our DNA is descended from? This organism is many many millions of years old and isn't even human.
The first two cases really don't mean much when looking at modern humans. For instance you could have gotten a fragment of Chromosome 1 from this person while I got a fragment of Chromosome 17 from this person (if we even got any DNA from him in the first place, which in itself is pretty unlikely), and it's perfectly possible that people living in East Asia preferentially got Chromosme 1 fragments from him while people in Europe got Chromosome 17 fragments from him (because his descendeds which moved to those locations carried those specific parts of his genome there).
Same with the second case, just because every human being at that point was both our's ancestors doesn't mean anything about what proportion of those ancestors we have and these proportions can be very different, from Wikipedia:
It's the third and further things which matter for how much genetic variance there is between two groups, becuase at that point you can directly point to specific portions of the genome and say that for both of us that ancestor provided the DNA at this location.
Those numbers are way too low.
The 3000, if you read the link you put, is using a way oversimplified model.
The 7000 is clearly false given the separation of the Americas long before that, and very low rates of admixture since aside from the last 500 years.
You don't actually need to have any DNA from any specific people generations back in your ancestry, the recombination could and often does go the wrong way.
Your overall point is good, though, that things go far enough back to matter, and that mere common ancestry doesn't mean an enormous amount.
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