I wouldn't worry about it. If they don't like the picture they will request a different one. More than likely the message was just a standard reminder of acceptable positioning.
Lots of pertinent details can be gleaned from posts that aren't anonymous by checking a user's FB profile and past group post history. If they want real privacy they can lock their profile.
No reputable clinic, hospital, or doctor is going to provide paperwork without seeing you in person for diagnosis, treatment plan, medication, and ongoing care appointments.
I hope you can take better photos of your passport pages than this picture you posted. The embassy asked for "high quality" photos. Do not cut off the edges of the passport pages, frame the pictures slightly larger than the pages.