This forum is very… convenient. As soon as I post a question here, I invariably find the answer by myself within a few hours.
One solution to my problem was to edit the /wp-includes/script-loader.php file. I changed the line
$styles->add( 'media', '/wp-admin/css/media.css'), array(), '20081210';
to
$styles->add( 'media', '/wp-admin/css/media.css');
and now it’s working. Maybe not the best solution? Perhaps changing the date (?) would’ve worked too? Oh well.