@Jack's article was in the context of Square. At Square, the merchants are the customers, and the merchant's customers are probably classified as the users. In that context, referring to merchants as users might be less precise.

When talking about twitter, I'm absolutely not their customer. I'm their user, and totally agree with your assessment.

One thing absent from @jack's article was a definition of customer:

cus·tom·er/ˈkəstəmər/ Noun: A person or organization that buys goods or services from a store or other business.