Index: src/wp-admin/includes/class-wp-site-health.php
===================================================================
--- src/wp-admin/includes/class-wp-site-health.php	(revision c2fd19e12d1ef741d4ad8f9ce8a20e975a4cb611)
+++ src/wp-admin/includes/class-wp-site-health.php	(date 1553378121698)
@@ -28,8 +28,6 @@
 	public function __construct() {
 		$this->prepare_sql_data();
 
-		add_action( 'wp_loaded', array( $this, 'check_wp_version_check_exists' ) );
-
 		add_filter( 'admin_body_class', array( $this, 'admin_body_class' ) );
 
 		add_action( 'admin_enqueue_scripts', array( $this, 'enqueue_scripts' ) );
Index: src/wp-admin/site-health.php
===================================================================
--- src/wp-admin/site-health.php	(revision c2fd19e12d1ef741d4ad8f9ce8a20e975a4cb611)
+++ src/wp-admin/site-health.php	(date 1553380342544)
@@ -27,6 +27,9 @@
 
 $health_check_site_status = new WP_Site_Health();
 
+// Start by checking if this is a special request checking for the existence of certain filters.
+$health_check_site_status->check_wp_version_check_exists();
+
 require_once( ABSPATH . 'wp-admin/admin-header.php' );
 ?>
 
Index: src/wp-admin/includes/class-wp-site-health-auto-updates.php
===================================================================
--- src/wp-admin/includes/class-wp-site-health-auto-updates.php	(revision c2fd19e12d1ef741d4ad8f9ce8a20e975a4cb611)
+++ src/wp-admin/includes/class-wp-site-health-auto-updates.php	(date 1553379756712)
@@ -101,7 +101,7 @@
 			array(
 				'health-check-test-wp_version_check' => true,
 			),
-			admin_url()
+			admin_url( 'site-health.php' )
 		);
 
 		$test = wp_remote_get( $url, compact( 'cookies', 'headers', 'timeout' ) );