Wouldn’t those with brown eyes still be related if they carried the recessive gene?

If you have blue eyes, you may be related to every other blue-eyed person in the world.
Researchers in Denmark have found that every person with blue eyes descends from just one “founder,” an ancestor whose genes mutated 6,000 to 10,000 years ago. Before then, everyone had brown eyes.

Lead scientist Hans Eiberg, a geneticist at Copenhagen University, began in 1973 to study a Danish father with 17 children who carried the gene for both blue and brown eyes. Over time, researchers were able to trace the blue-eyed trait to one specific area near a gene called OCA2. The paper appears in the journal Human Genetics.
Eiberg’s team then tested 155 blue-eyed people from Scandinavia, Turkey, Jordan and India, looking to see whether they, too, had similar DNA sequences on that gene. To their amazement, they found that each individual had identical DNA sequences in that region of that gene, an indication that the original mutation happened recently enough that it hasn’t had time to change.