Toby Ah.. but that looks like a fpm pool file -> probably from /etc/php5/fpm/pool.d/www.conf 😛
So the nginx user is indeed well.. nginx.
Personally, I would create a new pool and make the owner / group to whatever user you want owning the files. I circumvent a lot of permission stuff it seems that way. (Modifyed slightly for nginx webserver user.)
Here's a pool I have for my demo install of flarum where the very limited user demoflarum sends its php requests.
[demoflarum]
user = demoflarum
group = demoflarum
listen = /var/run/php5-fpm.$pool.sock
process.priority = -5
listen.owner = nginx
listen.group = nginx
pm = ondemand
pm.max_children = 1
pm.max_requests = 2000
pm.process_idle_timeout = 20s
chdir = /
Nginx related config
fastcgi_pass unix:/var/run/php5-fpm.demoflarum.sock;