This is a problem with WordPress initially, for not providing the option to allow/disallow comments on images, but the theme inevitably plays a role in it too. Themes that don’t support comments don’t have this problem. Of course, then they have the drawback of not supporting comments. :\
Anyway, this post helped me on a theme that does support comments. Ultimately, I ended up using the Comment Control plugin, referenced in that post. Probably a better solution than modifying the theme in most cases.