I don't see at all how that follows.
It's clear he broke the Japanese exit law (you have to show your passport to leave Japan by air, unlike, say, USA, France, Australia etc). Also he violated the terms of his house arrest. Likely some others.
But while I'm hardly an expert in Turkish or Lebanese law, in most if not all countries immigration authorities have wide discretion to admit or deny people on whatever basis they wish. And while it's easy to imagine someone in Turkey taking a bribe, that could very well be an unfair belief: it's just as easy to imagine the current Turkish government being happy to poke a finger in Japan's eye in some minor and deniable fashion. As for Lebanon, someone who is a national celebrity could easily make prior arrangement to be admitted with no bribe needed.