Firefox can't download private PDFs
Hudri's comment ultimately led me to the answer, so huge thanks!

The real issue is the mismatch between the file's real size on the server and the size Drupal stores in the file_managed table, filesize column. Firefox will only download files that have matching values for the HTTP response's Content-Length header and the real length of the file sent to the browser. As to why the value's greater than the real one I'm still finding the answer to.