Because if we assume she is right, and can prove it somehow, or Nijisanji believes her on her words alone, you will see another termination notice tomorrow. There is no other possible outcome of this being posted if it's not a lie. Therefore, there is no other motivation to post it. Also because woman being petty over being rejected and trying to get the man fired is extremely realistic scenario.
She has his words it happened. She has no evidence it really did. That's the difference. He could be venting to her and making shit up along the way, Niji would still fire him regardless if what he said was true, the intent is what matters.
