Yes, in the US at least, "a private club for members and their guests" is a common phrase, and would likely apply to a country club.

This would fit Digital Ocean's interpretation of private - not accessible to the general public, but accessible to other members.

Key concept is that members know it's just members and guests of members. DO does not make that clear, which is why people are getting upset.

That was the idea, yes. =)

I'm a little slow. Blast you and your Socratic method!