Just re-read your post.

Scenario 3 includes a population of Jokers. That is the difference.

So your assertion... is that Batmen only provide a benefit where there exist Jokers in the population. At least in the Volunteer's Dilemma.

Each of the scenarios 1 through 3 builds upon each other. The outcomes of 1 and 3 are similar, but in scenario 2 jokers are introduced into the mix, and in scenario 3 batmans are introduced to counteract the jokers.

...I believe the author is saying that if you have jokers, you need batmans to neutralize their effect.