Index: wp-includes/post-template.php
===================================================================
--- wp-includes/post-template.php	(revision 31229)
+++ wp-includes/post-template.php	(working copy)
@@ -635,7 +635,7 @@
 		$classes[] = 'no-customize-support';
 	}
 
-	if ( get_theme_mod( 'background_color' ) || get_background_image() )
+	if ( ( get_theme_mod( 'background_color' ) && get_theme_support( 'custom-background', 'default-color' ) != get_theme_mod( 'background_color' ) ) || get_background_image() )
 		$classes[] = 'custom-background';
 
 	$page = $wp_query->get( 'page' );