Distant genealogy gets pretty wacky. For example, consider at this range (30 generations), assuming that there wasn't overlap and inbreeding among all the lines that led to the President (which there was), he would have had 2 raised to the 30th power ancestors. That is 1,073,741,824. Over a billion. There weren't even actually a billion people in the whole world yet.
Virtually any who can fully trace their ancestry for 30 generations is almost guaranteed to have multiple relations with anyone else, at least from the same continent.
I know. We already know that everyone is descended from Lucy but Robert Mugabe from Zimbabwe is the only surviving, direct descendant which is why he has a legitimate claim to the entire planet...sorry to digress. I'm just desperately searching for some way to defend my property rights.
And without just one of them in the line, not one of us would be here. Think on that one for a second. Just one, one person missing and we are not born. Simple maybe a stupid thought? Yes, but I say its a amazing a lot of people are even here. There were wars, plagues, starvations and what not.