He's preferred by the teacher, yes, but he still essentially only takes the combat skills from his training. He is shown to have a sense of honor, but the episode sets up the idea that the honor was something he more or less already had, which is why he responded to the teaching better. And, after he leaves, he then supplements what he learns with his own means. He's not dressing himself in a ninja garb, he's not fighting people with asian weapons, he doesn't try to live his life in the way of a martial arts master in Asia etc.
So while this one individual episode does veer into that kind of of white savior-y territory, the rest of the stories are what keep it out of that. If every single TAS episode was constantly referencing that Batman was trying to live the way of ninja or something, that would be another story. But it doesn't.
