Attacking someone that is using the Ring
You were correct; the attacker determines the stat used.



The Ring reads:


  If you attack an opponent that has a Sanity trait, you can attack with Sanity instead of Might.


As it states, one can only use the Ring when taking the attack action. If someone is merely the subject of an attack, they may not use the Ring.

As usual, the attacker determines the stat used for both the attack and the defense. In this case, Might is used by both the attacker and the defender.