Remover «cap update_core» a Usuario

Hola, tengo un problema, por que en una instalación de prueba de WP, quiero quitarle la capacidad de actualizar el core, pero no puedo, se sigue viendo igual. Pero si se lo quito al ROL si funciona.

Nota: Se lo estoy quitando al Usuario 1.

Este es mi código:

<?php

/*
Plugin Name: RC Utilities
Plugin URI: http://URI_Of_Page_Describing_Plugin_and_Updates
Description: A brief description of the Plugin.
Version: 1.0
Author: Renzo Carlos
Author URI: http://URI_Of_The_Plugin_Author
License: A "Slug" license name e.g. GPL2
*/

//add submenu page in options
function rc_utilities_create_submenu() {
    add_submenu_page(
        'options-general.php',
        __( 'RC Utilities', 'rc-utilities' ),
        'RC Utilities',
        'manage_options',
        'rc-utilities',
        'rc_page_render'
    );
}
add_action( 'admin_menu', 'rc_utilities_create_submenu' );

//create a panel options for RC utilities
function rc_page_render(){
    include plugin_dir_path( __FILE__ ) . 'rc-utilities.php';
}

//registred group options
function register_mysettings() { // whitelist options
    register_setting( 'rc-option-group', 'rcu-options' );
}
add_action( 'admin_init', 'register_mysettings' );

//Obtain all options
$rcu_options = get_option('rcu-options');

//option disable update core
if ( isset($rcu_options['dis_upd_core']) ){
    add_filter( 'auto_update_core', '__return_false' );
}

//option allow minor update core
if ( isset($rcu_options['allow_min_core_upd']) ){
    add_filter( 'allow_minor_auto_core_updates', '__return_true' );
}

//option allow update plugins
if ( isset($rcu_options['allow_upd_plugins']) ){
    add_filter( 'auto_update_plugin', '__return_false' );
}

//option allow update themes
if ( isset($rcu_options['allow_upd_themes']) ){
    add_filter( 'auto_update_themes', '__return_false' );
}

//hide message of updates for all but no admin
if ( isset($rcu_options['allow_alert_upd']) AND $rcu_options['allow_alert_upd'] == 'no-admin' ){
    function hide_update_notice_to_all_but_admin_users()
    {
        if (!current_user_can('update_core')) {
            remove_action( 'admin_notices', 'update_nag', 3 );
        }
    }
    add_action( 'admin_head', 'hide_update_notice_to_all_but_admin_users', 1 );
}else{
    function hide_update_notice_to_all()
    {
        remove_action( 'admin_notices', 'update_nag', 3 );
    }
    add_action( 'admin_head', 'hide_update_notice_to_all', 1 );

}

//remove capability for update core
if (  $rcu_options['capability_upd_core'] == 'for_me' ){

    function remove_cap_update_core(){
        $user_id = 1;

        $user= new WP_User( $user_id );
        $user->remove_cap('update_core');

    }
    add_action('init', 'remove_cap_update_core');

}