Actually Facebook does admit once you change the setting that the mutual friends thing is related to that mutual friend's setting.
Here is how it works:
-If he/she has the same setting as you, meaning
only me setting, then no one sees that you are both mutual friends except both of you.
-If you changed your setting to
only me and the mutual friend to
friends only then your friends will see him/her as mutual friends with you.
Also there is a note under the Friends list privacy stating:
Remember: Your friends control who can see their friendships on their own timelines. If people can see your friendship on another timeline, they'll be able to see it in news feed, search and other places on Facebook. They'll also be able to see mutual friends on your timeline.