Yes. Exactly. That is the purpose of selling memberships: to control or limit who is part of your club, business or organization.
If not, why would they? They're not raking in billions in profit from the membership fees. It's the exclusivity of being a member and the benefits that come with it. What a "club" giveth, they can taketh away.
Hey, I've been a happy Costco member for almost 30 years. But I'm also far younger than 60, so whatever... I get to shop. π