If it's an image it can be shared AFAIK. Check this screen shot from my feed: https://www.dropbox.com/s/j779fmt85cb9mq6/Screen%20Shot%2020...

When clicking on "Share" I can share it to all my friends on my time line (or if my default were public, it would share to everyone).

From eyeballing my feed just now it looks as though any post that's a link can be shared. Then, the link is shared "via X." But only a public status itself gets the share button.