That is the title, not group membership. It only works if you are dealing with a single group and force title, which I kind of am, but for some reason some users did not get the title (and there is no “reset” action)
We already have this problem on meta … some with our customers that have the customer title, but we would like to see the actual customer group name on the card.
This is very common for small groups management and people moving from a mailing list world, we already have the site setting for: default categories watching which can not be used for this cause they are secure categories.
We also have Default notification level for group messages which is not usable on categories.
We already have 2 ways to force people into watching we ship, and both do not fit this need.
I guess an alternative here is Welcome to the amazing group automatic PM or notification we could send to every member that becomes a member of the group (optional), which teaches them about the group and how to click the “circle” so they can watch the group categories if they want to. I am not against this, I think it could help.
The problem is teaching this at scale. The default of watching is a better default for certain configurations of people.