The Administrative Procedure Act analysis is, I believe, correct. The Second Circuit did not give the agency proper deference wrt its fact finding and its adjudication. But the Court ducked the real question of whether the Constitutional analysis under Pacifica remains valid on the grounds that the lower court did not address the constitutionality of the FCC's decision. But the lower court only refrained from addressing this because lower courts don't address constitutional issues if they can avoid it.
Looks like they remained for a constitutional anlysis.