Force pdf download not working when include blog-header.php

I think WordPress is having problem with the url of your external script and throws a 404 error from the handle_404() function in the wp class in /wp-includes/class-wp.php

You can try to overcome that using for example status_header(200)

<?php
define('WP_USE_THEMES', false);
require('../wp-blog-header.php');
status_header(200);
header('Content-type: application/octet-stream');
header('Content-Disposition: attachment; filename="file.pdf"');
readfile('file.pdf');
?>

ps:

It is informative to look at the source for the WordPress query setup wp() that is called from the file wp-blog-header.php.

This function is defined in /wp-includes/functions.php and looks like this

function wp( $query_vars="" ) {
    ...cut...
    $wp->main( $query_vars );
    ...cut...
}

where

 function main($query_args="") {
    ...cut...
      $this->handle_404();
    ...cut...
}

and

 function handle_404() {
    ...cut...
    // Guess it's time to 404.
    $wp_query->set_404();
    status_header( 404 );
    nocache_headers();
    ...cut...
}

is from the wp class in /wp-includes/class-wp.php.