You can't "recruit" the Survivor. Imagine it's 4/3/1.
Mafia: I'm Mafia. Survivor, you will help us no-lynch, because if you don't, we WILL kill you tonight, and you lose. If you do, you're guaranteed to win with us.
Now the Survivor could try to call his bluff and risk it, but why? He has absolutely no reason to put his neck out for Town here and throw away a 100% win. So 4/3/1 is a loss for Town.
So 6/3/1 is lylo if Town tries to lynch Mafia, and has a 3/9 chance of doing so. If instead, they lynch the Survivor, then the next day they'll be at lylo, but with a 3/8 chance of lynching Mafia. Better odds, and one less Townie to mislynch. Sounds like optimal Town play to me.