I have been spending few hours on that issue and despite the high number of posts related to it, I cannot solve it. I have a Fedora 20 box with Nginx + PHP-FPM that worked q
This could also happen if there is no index.php in your vhost document root.
Carefully double-check the www_root parameter in your nginx configuration. Then double check that the php file you're trying to hit is actually in there.
In my case, I mis-typed the vhost doc root path and so pointed it to an empty directory, yielding a 403.