Calling them lunatics is just giving yourself a justification for any argument you want. They clearly aren't lunatics; they have - what appears to them - to be an entirely justified and moral system of belief.
When you help stage the coup against MacNamara in New Vegas you do it through the actual legislation of the Brotherhood. Hardin doesn't just march in and challenge him to a trial by combat. Why didn't the Outcasts do that against Elder Lyon's? From his lines it sounds like anyone can challenge the Elder and the determining factor is whom beats the other in a fight, there doesn't sound like the capacity to refuse - if the Elder wins then he's clearly the best and if the challenger wins then he is. What a stupid idea.
And yeah, he get's to skip a rank of Sentinel to achieve this.