Index: wp-content/themes/twentytwelve/functions.php
===================================================================
--- wp-content/themes/twentytwelve/functions.php	(revision 21435)
+++ wp-content/themes/twentytwelve/functions.php	(working copy)
@@ -316,7 +316,7 @@
 	// Translators: 1 is category, 2 is tag, 3 is the date and 4 is the author's name.
 	if ( '' != $tag_list ) {
 		$utility_text = __( 'This entry was posted in %1$s and tagged %2$s on %3$s by %4$s.', 'twentytwelve' );
-	} elseif ( '' != $categories_list ) {
+	} elseif ( '' != $categories_list && twentytwelve_is_categorized_site() ) {
 		$utility_text = __( 'This entry was posted in %1$s on %3$s by %4$s.', 'twentytwelve' );
 	} else {
 		$utility_text = __( 'This entry was posted on %3$s by %4$s.', 'twentytwelve' );
@@ -333,6 +333,25 @@
 endif;
 
 /**
+ * Returns true if a blog has more than one category.
+ *
+ * (Cribbed from _s theme.)
+ *
+ * @since Twenty Twelve 1.0
+ */
+function twentytwelve_is_categorized_site() {
+	$non_empty_categories = get_categories( array(
+		'hide_empty' => 1,
+	) );
+
+	if ( is_wp_error( $non_empty_categories ) || empty( $non_empty_categories ) || count( $non_empty_categories ) < 1 )
+		return false;
+
+	return true;
+}
+
+
+/**
  * Extends the default WordPress body class to denote:
  * 1. Using a full-width layout, when no active widgets in the sidebar
  *    or full-width template.