Why doesn't chown -R root:www-data work on my Wordpress installation?

Quite some time ago, I was following this tutorial which showed me how to install Wordpress on an NGINX + Ubuntu (LEMP) setup:

https://www.digitalocean.com/community/tutorials/how-to-install-wordpress-with-nginx-on-ubuntu-14-04

I got stuck on this portion for quite some time back then as I used root as the user for this instruction snippet below:

The group that nginx operates under is www-data. For the user portion, enter your user account name. We will demonstrate with an account called demo here:

sudo chown -R demo:www-data /var/www/html/*

To clarify, it didn’t give me any errors or anything, but what I found out was that if I used root:www-data for my file ownership settings, I wouldn’t be able to add / update plugins / edit code on the site. It would always prompt me for FTP / SFTP details, in which it would fail even if i entered the correct credentials due to the permissions being drwxr-xr-x (Owner has write permission).

So i tried this:

sudo chown -R www-data:www-data /var/www/html/*

and it worked – I was able to write / update plugins freely as the Wordpress site admin.

However, I now have a roughly better understanding of how ownership and groups work, and I’m concerned that by doing chown -R www-data:www-data, I opened a security flaw on my own.

Am I doing it right? Why didn’t root:www-data work for being able to update the site in the first place?