How to do Basic URL Rewrite Without Redirecting

If I use the simple code below:

function my_custom_rewrite_rules() {
    add_rewrite_rule(
        '^rewriteme$',
        'index.php?page_id=1',
        'top'
    );
}
add_action('init', 'my_custom_rewrite_rules');

I would expect to be able to visit http://example.com/rewriteme and see the content of the Hello World post while keeping /rewriteme in the address bar. It doesn’t work, though. It actually redirects to http://example.com/hello-world/.

How do I get it to display the content of the Hello World post without actually changing the URL in the address bar?

(And yes, I’ve flushed rewrite rules.)

If you just want to see the content of the /hello-world post on /rewriteme page you can try to add something like this on the page.php of your theme:

<?php
    if (is_page('rewriteme')) {
        // query for the about page
        $your_query = new WP_Query( 'postname=hello-world' );
        // "loop" through query (even though it's just one page) 
        while ( $your_query->have_posts() ) : $your_query->the_post();
            the_content();
        endwhile;
        // reset post data (important!)
        wp_reset_postdata();
    }
?>