It's probably something WP has obfuscated under the guise of "being helpful". I suspect the permalink is to the "media page" which contains the PDF, but not the PDF itself. In that case, it would take some digging. I would use the get_post filter to see what custom fields are available on that item -- digging around to see where the #!$%! wp buried the data you need is much easier in PHP, so I would do something like this:
$rel = get_custom_field('customfieldname:get_post');
// OR more raw yet
$post_id = get_custom_field('customfieldname:raw');
print_r will show you what fields are available in the related object, and from there you can see if there's anything helpful to you.