Very few people go on Facebook to go to a specific group for a browse. They end up on there as a result of their feed which they're using. Consequently, people end up using Facebook more than other sites through a mixture of convenience and conditioning.
If Facebook was used intelligently and with guidance, it's an excellent source of driving people to an external website.
Any content on Facebook relating to the club should link to the relevant information on the club site. As an example, "hey guys, quick update on venue change can be found here. To see more information or ask questions please click the link." But, laziness and lack of interest to invest 30 seconds into a post means it doesn't happen.
Of course, one way around that is for the club to create all of the local groups on Facebook and add admins to the group. That way they can offer guidance and support when needed, have the option of mass posting/advertising for national events and prevents the issue of no one being in control of a local group page.