Only option is if 'joe bloggs' hides themselves from people via blocking them. With some super strict settings people can just see a name not a picture. Also i think you can make it so you cant have friend requests, but only send? So my mum told me, i never looked into that though, i just nodded n walked off.
Other nifty trick is you can hide your wallposts & photos from people.. but have them as a friend by setting up privacy groups.. great way to slagg off tutors and not have them see it!