All these people have one friend in common with this person, maybe they know each other as well? Being a psychiatrist or whatever has nothing to do with it.
EDIT: I stand corrected. Not so simple regarding where they get the "potential friendship" data from. Diagonal reading mistake on my part.
I mean, I guess you could keep those contacts in a note or some other record outside your contacts list, and just tap to call or email or whatever. But that only works as long as the Facebook app doesn't decide it needs access to that kind of record, too. And when you find yourself going that far out of your way to circumvent something that's installed on your phone, maybe it's time to think about whether that thing is more trouble than it's worth.