The full paragraph you're excerpting from Wikipedia is much less convincing:
> Such groups can include the press (akin to the European 'Fourth Estate'), the people (in sum or as grand juries), and interest groups. The independent administrative agencies of the United States government, while technically part of any one of the three branches, may also be referred to as a ‘fourth branch’.
Anyone using the expression to refer to "the people" or "the press" obviously isn't talking about those groups' legal relationships to the de jure branches of government. My sense (from the Wikipedia article, but also anecdotally) is that "fourth branch" is just a colloquial way to refer to various sociopolitical groups. So I don't see this as a convincing rebuttal to dragonwriter's comment.
> Such groups can include the press (akin to the European 'Fourth Estate'), the people (in sum or as grand juries), and interest groups. The independent administrative agencies of the United States government, while technically part of any one of the three branches, may also be referred to as a ‘fourth branch’.