Wordpress REST API "rest_authentication_errors" doesn't work external queries?

I was using following experimental codes for experimental purposes.

add_filter('rest_authentication_errors', 'auth');
function auth() { return true; }

add_action( 'rest_api_init', 'cors', 15 );
function cors() {
    add_filter( 'rest_pre_serve_request', function( $value )
    {
        header( 'Access-Control-Allow-Origin: *' );
        return $value;
    });
}

Then I realized that if we made a request between two separate servers, the API's response failed. However, we have set all requests to be "correct" with the "rest_authentication_errors" filter and have accepted all connections from "*".

• If we send a "POST" request from "a" to "b", it says "authorization failed".
• But if we make a request from "a" to "a", the query works.