Index: wp-content/themes/twentytwelve/functions.php
===================================================================
--- wp-content/themes/twentytwelve/functions.php	(revision 21432)
+++ 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_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 +333,48 @@
 endif;
 
 /**
+ * Returns true if a blog has more than one category.
+ * 
+ * (Cribbed from _s theme.)
+ *
+ * @since Twenty Twelve 1.0
+ */
+function twentytwelve_categorized_site() {
+	if ( false === ( $all_the_cool_cats = get_transient( 'twentytwelve_all_the_cool_cats' ) ) ) {
+		// Create an array of all the categories that are attached to posts
+		$all_the_cool_cats = get_categories( array(
+			'hide_empty' => 1,
+		) );
+
+		// Count the number of categories that are attached to posts
+		$all_the_cool_cats = count( $all_the_cool_cats );
+
+		set_transient( 'twentytwelve_all_the_cool_cats', $all_the_cool_cats );
+	}
+
+	if ( '1' != $all_the_cool_cats ) {
+		// This site has more than 1 category so twentytwelve_categorized_site should return true
+		return true;
+	} else {
+		// This site has only 1 category so twentytwelve_categorized_site should return false
+		return false;
+	}
+}
+
+/**
+ * Flush out the transients used in twentytwelve_categorized_site
+ *
+ * @since Twenty Twelve 1.0
+ */
+function twentytwelve_category_transient_flusher() {
+	// Like, beat it. Dig?
+	delete_transient( 'twentytwelve_all_the_cool_cats' );
+}
+add_action( 'edit_category', 'twentytwelve_category_transient_flusher' );
+add_action( 'save_post', 'twentytwelve_category_transient_flusher' );
+
+
+/**
  * 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.