I think I know why some Facebook profiles do not show up as a link with a picture. Many people have followed tutorials on how to lock down their Facebook privacy settings. You may want to ask your good friends to allow apps to see pictures and status updates.
1. on Facebook.com go to Account -> Privacy Settings
2. click the link "Edit your settings" at the bottom under "Applications and Websites"
3. click the button "Edit Settings" for "Info accessible through your friends"
4. check mark Bio, My status updates, and My photos
5. Save Changes