proprietary

A  proprietary  API typically has one or more of the following characteristics: single implementation (one silo or browser engine), company controlled, or company-specific terms of service (TOS).
 * one-off - only works on one site / silo
 * owned / controlled by a single company - or at best a few companies, an oligopoly as it were.
 * nasty TOS - a terms of service that is unfriendly to developers and users, often forcing them to give up numerous rights, placing unnecessary burdens upon them (e.g. you must display data in such and such a way)

By contrast, an open API or protocol is typically:
 * interoperable — it works on multiple sites, with multiple implementations (browser engines), testable with an open test suite
 * developed in the open — i.e. decision-making processes are open for consumers to observe and influence with, reference implementations are available to the general public for free (as in beer+freedom)
 * unencumbered by TOS or patents — licensed under a liberal license, royalty free patent policy (e.g. W3C Patent Policy)

What does owned or controlled mean
Q: What, in practical terms, does it mean for one or more companies to “own” or “control” an API?

A: “control/ownership” in this case refers to:
 * decision-making processes being hidden from + excluding, therefore disempowering, consumers of the API
 * reference implementation being closed-source
 * official documentation being authored exclusively by the controlling organization

Is Twitter API proprietary
Q: Is the Twitter API proprietary even though status.net implements it?

A: Yes it is proprietary because:
 * 1) Twitter owns & controls it, i.e. the decision-making processes and reference implementation are completely closed to consumers, and the documentation is controlled by Twitter.
 * 2) It has a nasty TOS - e.g. display requirements

Previously:
 * 1) Status.net did not "implement it". Status.net implemented some subset of the old Twitter API. In essence Status.net had an API that was based on a clone/fork of an older version of the Twitter API.