“Your neighborhood gossip is a purveyor of ‘news,’ but it's not likely that anybody would seriously consider her to be part of ‘the press’ in any legal sense of the term.”
You are defining “the press” as an institution, e.g. the Newspaper/magazine industry — or the news media. I don't believe the First Amendment is addressed to any such class specifically.
A Gospel tract society, a church, synagogue, mosque, or any religious persons, for example(s) can purchase a “press” and produce and distribute literature propagating what it believes to be the truth, and Congress can not make a law abridging that right, because that is included in the concept of “the press.” The First
Amendment is not at all specifically dealing with “news” sources.
Any individual can purchase a Risograph or a Xerox machine, interface his computer, and run off thousands of copies of literature in an effort to be elected to the city council, and Congress can make no law to abridge that right, because that is also included in the concept “the press.”
Anyone can start-up a local publishing business to, say, reprint out-of-print books that are now in the public domain, on any subject anyone might be interested in. Congress can make no law to abridge that right, because that also is included in the concept of “the press.”
I can write, publish, and distribute Creationist, anti-Darwinian, anti-Humanist Christian school and home school curriculum, and Congress cannot make a law to abridge my right to do so, because that is also included in the concept of “the press.”
To limit the concept of “the press” to news sources is absolutely absurd.
The key words there are "you don't believe." "The press" is not clearly defined in the First Amendment. The term must be defined in cases like this one, which hinge directly on the woman's claim to be covered by that designation.
The principles of "liberty of the press" were defined by the likes of David Hume:
If the passion of the ministers lie toward peace, our political writers breathe nothing but war and devastation, and represent the specific conduct of the government as mean and pusillanimous....As long, therefore, as the republican part of our government can maintain itself against the monarchical, it will naturally be careful to keep the press open, as of importance to its own preservation.
Hume's sense of "the press" is clearly an institutional one; we have a similar sense of the term when we acknowledge the media as the "fourth estate." Neither Hume nor the Founders considered "freedom of the press" to be license to say whatever they pleased, of course: the media are properly subject to being sued for libel and/or slander.
The First Amendment is not at all specifically dealing with “news” sources.
True -- indeed, as per Hume, the original intent was to protect political writers' right to oppose the government, as opposed to "news reporting."
As you properly pointed out, if we take the Constitution literally on the point, "the press" could only refer to printed material -- which, at the time, was the only medium available other than political speech (which is also and separately covered by the First Amendment). We don't take the term literally anymore, of course -- there are too many other media which satisfy the spirit of what Hume, et al. were talking about.
But at the same time, that very reliance of the spirit over the letter of the clause, forces judges to rule on what is, and is not, covered under the "freedom of the press" clause.
The underlying legal question in this case is straightforward: In a legal sense, what distinguishes "the press" from a gossip? There is a difference; but what are the specific criteria by which one would make the distinction?
It's not the judge's fault we're discussing "news sources" in this particular case. The defendant seems to be claiming that she is a "news source," and as such is entitled to protection of her sources on the same basis as the New York Times.
The judge, then, is required to rule on whether or not she is truly a "news source" in the First Amendment sense of the term -- or if she's merely a gossip, as the plaintiffs claim.