Correct. ND should have told Manti that a man of character who also represents the ND institution should tell the truth immediately, especially to the media, where the light shines brightest.
First off, it was Manti who told ND about the situation, so questioning his character makes little sense in this regard, he outed himself I guess is what you are saying. Second, with the NC game looming, it would be stupid to create the media frenzy we are seeing unfold right now. Third, I believe it was stated somewhere, and if I find the article, I'll link to it, that ND did encourage Teo to get out in front of the story lest the narrative be wrestled away from him like it has. He probably should have addressed it then, but he, his family or his advisors made a tactical decision not to.