Well, I say they can and they do. When you enter the lovely world of voice prompts after calling customer service, you get to choose whether you are calling about your TV service or internet service.
To me, that is classifying customers. When you have services available to those intelligent enough to find your back door services, such as Twitter and @comcastcares, you are classifying customers.
Read more: Comcast says they can't classify customers for service [click]