The article treats the 'open' and 'closed' status of APIs as if it somehow relates to being open-sourced or something. Really they are just referring to access control, which is both irrelevant to the issue at hand (whether an API is copyrightable) and also not at all relevant to the actual APIs being discussed (Java). Access rights for linked APIs mostly don't exist, and if they do its by way of authorizing the runtime the library is running within, not by using security tokens + authentication.
