After some research it turns out systemd uses the file below to startup nginx
The file on Ubuntu 15.04, Ubuntu 15.10, and even the nginx site itself say to use the After line like below
This makes a person think that the network should up and ready to go. However, I found the link http://www.freedesktop.org/wiki/Software/systemd/NetworkTarget/ that says
network.target has very little meaning during start-up. It only indicates that the network management stack is up after it has been reached.
The link goes on to say
network-online.target is a target that actively waits until the nework is "up", where the definition of "up" is defined by the network management software.
So I changed the After use that instead like
Now nginx starts up fine on bootup. I am not claiming this is the fully correct solution as it is possible that a different After target should be used that would be more correct in some other way, but this seems to work for the last couple of reboots.