It doesn't work that way, actually. Recombination during meiosis is pretty random.
A simplified example: mom is 100% scottish, dad is 100% german. (Not real life, no one is 100% anything).
You can end up almost 100% scottish, almost 100% german, and any combination in between, depending on how the DNA recombined.
Now add in sibling results: you can see something like 30% particular ethnic DNA, for example, while a sibling can get 0%. And so on.
So, it is theoretically possible that the old guy and his a bit distant relative could have very similar DNA.
Not likely, but possible.