And violation of those laws is a threat to the freedom of the press.

Let's consider a hypothetical but plausible example: A billionaire named Elon Bezos is tired of journalists exposing his illegal schemes so he hires the Pinkertons to stalk and harass journalists, dox them and post their personal information on 4chan with claims of those journalists working for the pizzagate illuminati, and threaten their friends and family with life ruination and murder. In this hypothetical everything done is illegal and none of it was done by the government; would you therefore earnestly conclude that none of it constitutes a threat to the freedom of the press? Ludicrous.

You need to stop conflating the First Amendment with freedom of the press. The First Amendment is one law that aims to protect the freedom of the press from one specific kind of threat; threats coming from the government. It does not preclude the existence of other kinds of threats to freedom of the press.