He absolutely did not.
He went before CSAC and claimed that not only did he apply for a TUE, he was given an exemption from Nevada. Specifically, made up a crazy lie, because this was not true. He also had a internal medicine doctor (not an endocrinologist) as a witness state that Chael needed testosterone because he never went through puberty. It was absurd.
When he went before NSAC, he capitulated and admitted to lying and blamed it on Matt Lindland and confusion. Of course, again, absurd lies and he went before Nevada hat in hand.
Fast forward to his next suspension, Chael gets busted for estrogen blockers. Instead of admitting doping, he goes on the offensive in the media, claiming he was simply taking this medication as prescribed to him in his attempt to father a child with his wife. He really doubles down on this.
Of course, they randomly surprise tested him again shortly after, and he tests positive for HGH, EPO and hCG. Sonnen then is fired from both the UFC and Fox, for being a habitual, pathological liar and cheater.
Sonnen is entertaining, and he is most definitely clever and a fun broadcaster - this weird notion that he 'came clean' is like living in upside down world. This guy lied and lied and lied through his teeth until he was literally kicked out.