What I don't understand is how they can say the blue-eye mutation occurred in one single individual. I would think it is just as possible that the mutation could have occurred multiple times, and thus there would be multiple origins to those with blue eyes.

I did find a different source that would tend to support the randomness of mutations, and that also indicates that there are two different mutations that can lead to blue eyes, and as such, it is unlikely there is only one ancestor. http://www.thetech.org/genetics/ask.php?id=160