The courts have held that government can restrict free speech to further national security, so it's not novel. At the same time, proving a relationship between media corporation misinformation and the insurrection would be very difficult.
Periodically, the Supreme Court has examined whether the government can restrict speech to further the compelling interests of national security. In doing so, the Court has recognized that national security, as a governmental interest, does justify restrictions on First Amendment rights. In the landmark free press decision Near v. Minnesota (1931), the Court established a general rule against prior restraints on expression. However, the Court did note that the government could shut down a newspaper if it published military secrets: “No one would question but that a government might prevent actual obstruction to its recruiting service or the publication of the sailing dates of transports or the number and location of troops.”
Nevertheless, the government must provide proof that national security interests really are in play—that is, the government cannot simply use national security as a blank check to sidestep constitutional challenges. In New York Times Co. v. United States (1971), the majority of the Court rejected the government’s national security justifications for attempting to prevent the New York Times and the Washington Post from publishing the Pentagon Papers, the top-secret history of the U.S. involvement in the Vietnam War. In his concurring opinion, Justice Hugo L. Black explained that “the word ‘security’ is a broad, vague generality whose contours should not be invoked to abrogate the fundamental law embodied in the First Amendment.”
https://www.mtsu.edu/first-amendment/article/1134/national-s...