Section 8(c) did most of the heavy lifting. It provides:
29 U.S.C. s 158(c). The Court essentially applied a First Amendment free speech style of analysis to the issue.
Ultimately, the Court concludes that the 8(c) right to express views without incurring an unfair labor practice charge includes a right to keep silent (framed another way, a right against compelled speech). As the NLRB's poster requirement treated failure to post as an unfair labor practice, or evidence of union animus in an unfair labor practice charge, the rule violated s 8(c).
The NLRB did have another method of enforcing the rule, which was to toll the statute of limitations. The Court held that the NLRB lacked authority to modify the statute of limitations, so that portion of the rule was vacated as well.
Could it get any worse for the NLRB's poster requirement? Well, yeah, actually it can. Although the Court's controlling (and unanimous) opinion did not reach the issue, a majority of the judges issued a concurring opinion. In it, the judges found that the NLRB would have lacked the authority to promulgate the poster requirement rule even if it had not violated s 8(c).
This may be the end of the NLRB's poster rule. They can press it in other circuits, but employers have the option to appeal NLRB rulings to their home circuit OR the D.C. Circuit. Guess where they'll be heading? The NLRB could appeal to SCOTUS . . . but this doesn't strike me as a SCOTUS-worthy case (maybe if there's a split on the issue with another circuit).
BONUS QUESTION: Since two judges, a majority of the D.C. Circuit panel, held that the NLRB lacked the authority to promulgate the rule . . . is that binding precedent in the D.C. Circuit?
Image: NLRB logo used in commentary on the NLRB. Not Official Use.