Is it true that all blue-eyed people in the world are related because we share the same common ancestor??

Question: Is it true that all blue-eyed people in the world are related because we share the same common ancestor??
- Keywords:
  ancestor,
  blue eyed,
  relation
Asked by ewensaxx to Christina, Colin, Jess, Samaneh, Steve on 19 Jun 2013.
- Jess Bean answered on 19 Jun 2013:
  
  That idea seems pretty crazy but by the looks of it you are right! Between 6000 and 10000 years ago scientist think that everyone used to have brown eyes, but a mutation in someone’s DNA meant that no brown colour was produced, making their eyes blue!

Question: Is it true that all blue-eyed people in the world are related because we share the same common ancestor??