Yes, black hair can compliment brown eyes, but it is also dependent on a bunch of things like skin complexion and whether the person has a nice face or is cute or not.
Beauty isn't just about matching colors, it's how those colors are arranged on the face too.
It's like no one thought Picasso was a great artists because he used a really nice shade of red, it comes down to the overall image, and the message behind it.
Also there are a bunch of famous people that have black hair and brown eyes and are considered beautiful. That doesn't mean everyone with this combination is really good looking though:
But like I said, not everyone that has black hair and brown eyes looks like Kim Kardashian, so try and see behind the colors place.