Why add a minor to a PhD?
A minor gives a grad student the option of diversifying his/her learning experience. Much research is interdisciplinary (like stats and CS), so taking a few classes in another department can be very beneficial. It also gives a grad student an excuse to take courses in something that isn't directly related to their research. (Minoring in a foreign language or business can be generally useful, for example.) In my own experience, most grads minor in something closely related to their research. 

As far as I know, very few people look at a graduate student's minor. The biggest reason I can see for having a minor outside one's home department is to diversify one's educational background. 

I looked around to see what universities said about this. Georgia Tech states that "The purpose of the minor is to encourage a wider interest on the part of the student and to provide a broader basis for the evaluation of the student's capabilities." (source) Stanford requires a minor for its Education grads (source).