Matt Asay suggests that a definition for an open source company would be:
An open source company is one that, as its core revenue-generating business, actively produces, distributes, and sells (or sells services around) software under an OSI-approved license.
Nat asks a difficult question. One that I am frequently in the habit of posing, although not as straightforwardly. For example, the copyright notice for Windows XP (I haven't seen the one for Vista yet) advises us that
Portions of this product are based in part on the work of the Regents of the University of California, Berkeley and its contributors. Because Microsoft has included the Regents of the University of California, Berkeley, software in this product, Microsoft is required to include the following text that accompanied such software: