Nginx 403 forbidden for all files

I have nginx installed with PHP-FPM on a CentOS 5 box, but am struggling to get it to serve any of my files - whether PHP or not.

Nginx is running as www-data:www-data, and the default "Welcome to nginx on EPEL" site (owned by root:root with 644 permissions) loads fine.

The nginx configuration file has an include directive for /etc/nginx/sites-enabled/*.conf, and I have a configuration file example.com.conf, thus:

server {
 listen 80;

 Virtual Host Name
 server_name www.example.com example.com;


 location / {
   root /home/demo/sites/example.com/public_html;
   index index.php index.htm index.html;
 }

 location ~ \.php$ {
  fastcgi_pass   127.0.0.1:9000;
  fastcgi_index  index.php;
  fastcgi_param  PATH_INFO $fastcgi_script_name;
  fastcgi_param  SCRIPT_FILENAME  /home/demo/sites/example.com/public_html$fastcgi_script_name;
  include        fastcgi_params;
 }
}

Despite public_html being owned by www-data:www-data with 2777 file permissions, this site fails to serve any content -

 [error] 4167#0: *4 open() "/home/demo/sites/example.com/public_html/index.html" failed (13: Permission denied), client: XX.XXX.XXX.XX, server: www.example.com, request: "GET /index.html HTTP/1.1", host: "www.example.com"

I've found numerous other posts with users getting 403s from nginx, but most that I have seen involve either more complex setups with Ruby/Passenger (which in the past I've actually succeeded with) or are only receiving errors when the upstream PHP-FPM is involved, so they seem to be of little help.

Have I done something silly here?

One permission requirement that is often overlooked is a user needs x permissions in every parent directory of a file to access that file. Check the permissions on /, /home, /home/demo, etc. for www-data x access. My guess is that /home is probably 770 and www-data can't chdir through it to get to any subdir. If it is, try chmod o+x /home (or whatever dir is denying the request).

EDIT: To easily display all the permissions on a path, you can use namei -om /path/to/check