Index: src/wp-includes/class-wp-customize-control.php
===================================================================
--- src/wp-includes/class-wp-customize-control.php	(revision 31943)
+++ src/wp-includes/class-wp-customize-control.php	(working copy)
@@ -1243,14 +1243,11 @@
 class WP_Customize_New_Theme_Control extends WP_Customize_Control {
 
 	/**
-	 * Render the new control.
+	 * Render the control content.
 	 *
 	 * @since 4.2.0
 	 */
-	public function render() {
-		if ( is_multisite() || ! current_user_can( 'install_themes') ) {
-			return;
-		}
+	public function render_content() {
 		?>
 		<div class="theme add-new-theme">
 			<a href="<?php echo admin_url( 'theme-install.php' ); ?>" target="_top">
Index: src/wp-includes/class-wp-customize-manager.php
===================================================================
--- src/wp-includes/class-wp-customize-manager.php	(revision 31943)
+++ src/wp-includes/class-wp-customize-manager.php	(working copy)
@@ -1171,10 +1171,12 @@
 			) ) );
 		}
 
-		$this->add_control( new WP_Customize_New_Theme_Control( $this, 'add_theme', array(
-			'section' => 'themes',
-			'settings' => 'active_theme',
-		) ) );
+		if ( ! is_multisite() && current_user_can( 'install_themes' ) ) {
+			$this->add_control( new WP_Customize_New_Theme_Control( $this, 'add_theme', array(
+				'section' => 'themes',
+				'settings' => 'active_theme',
+			) ) );
+		}
 
 		/* Site Title & Tagline */