When trying to view the smileys in question as a mod or admin, the images display properly, but when viewed as registered user (using test permissions, and using a test user that I have for myself), I can verify that when viewing the attachment page, I get a permissions error. "You do not have permission to view this page or perform this action."
On this particular site, I just did the latest update to 1.5.8 over the weekend. This error (according to the user who reported it) is new, so perhaps there was something in the 1.5.8 update that caused this?
(screen shot of registered forum permissions)