This is what I ended up doing after all. This was a major problem in the backlog, with such an easy fix. Thank you!
On my multisite network, I have 3 sites. Each of those use the same theme. On one page of each site I show some news, and on each article, the author gets named, and his picture gets showed. So when I add his picture on site 1, it gets removed on site 3. I need to keep it there, and not have it removed when I add him to another site
http://jessheimhage.soloneiendom.no/visningsboliger-endelig-klar/
http://kolbotnhage.soloneiendom.no/byggestart-rundt-hjornet/
Both should have that little circle image
They are sites, bad phrasing on my part there
