A colleague made it run by adding the nginx user (www-data or http user) to the seafile group and chmod 0750 on the seafile home-directory. Maybe worth a try.
I tried didn't work. My fresh install is like the one in the manual.
what do you get when you visit
Sorry for my late reply. Maybe you can try chown the seafile directory to root and try to run nginx and seafile as root - just for a test. If it works it's a permission issue.
Actually it was a wrong path to seahub/media
and now I'm using Seahub without! fastcgi