Why can I not view image attachment pages?

From what you’ve described, it sounds like the theme doesn’t have an attachment.php template to handling displaying the actual attachment page.

You check on the attachment page, by going to Appearance->Editor, and checking for an attachment.php; however, I believe that answer is incorrect. WordPress should default to displaying the image on the normal blog index page, if I’m not mistaken. Which means the error could have something to do with a custom permalink structure.

Have you changed the permalink structure? If so, try changing it back to default and see if you still get a 404.