Index: wp-admin/includes/media.php
===================================================================
--- wp-admin/includes/media.php	(revision 21157)
+++ wp-admin/includes/media.php	(working copy)
@@ -965,7 +965,7 @@
 
 	foreach ( get_attachment_taxonomies($post) as $taxonomy ) {
 		$t = (array) get_taxonomy($taxonomy);
-		if ( ! $t['public'] )
+		if ( ! $t['public'] || ! $t['show_ui'] )
 			continue;
 		if ( empty($t['label']) )
 			$t['label'] = $taxonomy;