I've seen family go into denial on this and many other issues, not just a substance abuser. Depending on what generation or era they are from they're extremely private or worried about shame.
Outing someone is not the best idea but if their addiction and rehab explain things especially in a conversation that came up that's another. You can ask for confidentiality but the issue won't be a 'secret' much longer. You also might find out your predicament is not so unusual. Explain it , don't exploit it.