If you look at one generation ago one have 2 * 2 ^ 0 ancestors, at two generations, one have 2 * 2 ^ 1 ancestors, etc. At 27 generations one apparently has more ancestors than people in the world at that time. This apparent paradox stems from the fact that we are heavily inbred.
Thus the article is correct.
I'm not following your point - maybe it's just a linguistic thing. To me, inbreeding implies relation, at least blood-relation, even when there was no other relation, e.g. conquering armies raping and pillaging.
No argument with your math.
Perhaps you're off by a 0 or two...?
The Americas may have been clearly separated for a while, but they have done so much interbreeding with people from other continents since 1492, that the common ancestor is more recent than that.
"Monte Carlo simulations suggest the MRCA was born surprisingly recently, perhaps even within the last 5,000 years, even for people born on different continents."