There are a lot of mainstream media outlets (1st Amendment) that operate out of New York; is there any requirement for them to pass a test for accuracy?

From NEW YORK STATE RIFLE & PISTOL ASSN., INC. v. BRUEN

The constitutional right to bear arms in public for self-defense is not “a second-class right, subject to an entirely different body of rules than the other Bill of Rights guarantees.” McDonald, 561 U. S., at 780 (plurality opinion). The exercise of other constitutional rights does not require individuals to demonstrate to government officers some special need. The Second Amendment right to carry arms in public for self- defense is no different.

More on topic, Washington has no testing requirements.