I think different from hilllly friend. All of his goods he use: jacket, logo, hat....are belong to his A Man. They use them in cafeteria car or in any program to support their actors in company. A jacket, you can't say link to JS personality support Nara.
But to dating rumor is another story because someone in internal circle expose information but no one know who is someone and JS is main person in that news. Anyone want to lower his reputation will wonder who is someone or his A Man make that story to trendsetter their actor. But a jacket can't make this story or represent JS. Though A Man or JS use it to make everyone focus on Nara or her film, no one can say anything. 89 mansion cafe car had represented JS and A Man company and he send it to very many actor, no only Nara.