You can also run "oil refine install" (as root) on your project directory to set the correct rights.
And you potentionally missed one: If your app writes to config files, you also need to set write rights on fuel/app/config.
BTW, it is hardly ever a good idea to give "world" write rights, and it is hardly ever needed. If your nginx user is part of the group (which it should), than 770 should work fine too...