KBExit I have not watched the video but yes, that seems to be the way Flarum was originally intended to be configured.
There are 2 "official" ways to configure Flarum: the recommended one which is the default when installing via Composer is that the Flarum files will include a public folder, and the hosting configuration will be modified to set the /public path as the "document root" or "web root". This ensures that the webserver will never distribute or allow access to files that are outside the public folder. This is an approach used by many modern web applications like Laravel.
The other official method is to not have a public folder, place all Flarum files in a single folder and use Apache/nginx rules to protect the sensitive data. This is more of a "legacy" approach, the one notably used by WordPress for example. This approach is less secure, because if for any reason the security module gets disabled in Apache or nginx, now all files are exposed. On some hostings it's the only option if the "document root" cannot be customized. For this second method the easiest starting point is to download the Flarum Zip with "public path: no". The "Customizing paths" instructions in the documentation are only if you downloaded via Composer, or have an existing older forum you need to migrate to a hosting that doesn't support the public document root.
In either case, if you had already completed the Flarum installation wizard before fixing the configuration, you need to update the URL in config.php. For new forums ideally you should make sure the URL is properly configured before running the installation wizard.
I hope this makes things clearer.