Hmm. As far as I can tell, it's usually the silly 'rule' that if two or more bikes are going in the same direction, it's a race.

Then again, the bike club could simply let anyone lead, no matter how unstable. Bicycle Club of Philadelphia used such a person for their 'beginner's ride' a few years ago. One ride was enough to see they made a mistake. Later it came out the guy had a habit of changing routes mid course without telling other riders. One time he ended a ride early and didn't let the group know - he just got on a train with his bike and left. (Reminds me of the leader of the peach ride getting a lift from a driver and then leaving before all the riders were back at the start.)