Without supporting details, I doubt it. I also think that more than one gene controls eye color, and its occurance is more characteristic of a multiple gene trait.
We've often been told that dark eye color is rarer in people with certain developmental disorders. There have been repeated suggestion that the prevelance of blue eyes among people with certain disorders that feature problems with growth and development of the brain.
Therefore I think that there are several different ways in which blue eyes can occur - via developmental issues, via spontaneous mutation, via inherited genes.
There are also epigenes that control a whole group of genes and that's possible too.
Genetic mutations occur all the time, so I think that I would need to see the data from the study that suggested everyone inherited one gene from eons ago.
THat has been stated about red hair, that it arose from one single person who had a gene mutation in Europe several thousand years ago, but again, I'm not sure there aren't other possibilities.
A friend of mine has fairly pale, hazel-grey eyes. In some situations they show rather blue, in others, more greenish, in others more grey.
I think it's really cool. I never get tired of looking at him....lol.