I don't think it is a question of Facebook or a website. Maybe the title of my email gave that impression.
We can use both. Use Facebook for what it is good for (if that is anything), and use the web site for what it is good for. Creating events and managing RSVP might be something to leave to Facebook. Although, if we used one of the CMS software systems, it could probably do that job.
For instance, I use my personal Facebook site only to have links to my blog articles on my web site. I agree, that I want to own the data on my blog. All my photo albums are on my own website.
On the Facebook create group page there is an option to set privacy to:
Privacy: Open Anyone can see the group, who's in it, and what members post.
Actually, I suppose that may already be the setting. The description does not imply that you do not need to at least login to Facebook to see the group.