Yep, if there are zero members, then the statement "all members are vetted" is mathematically true. Well done.

In mathematics we would call this "vacuously true"

It's an absolutely lovely idea in theory, but I can see a small proportion of bad-faith actors absolutely ruining the experience for the rest. For example, how do you get overstaying guests to leave, what happens if there's suddenly a deluge of visitors on a holiday weekend and how do you say "you, not you"?

So, they're missing the V then.