The Miniride Principle?

While reading Regan, something struck me as odd: the concept of the miniride principle.

Regan basically states that the miniride principle means that every moral agent or patient has their own prima facie right. This basically means that my rights are no greater than the rights of the person sitting behind me or behind me at this very moment. Thus, when presented with the choice to violate one or all of our rights, a person must choose to violate only one. Our rights are all equal and so one must take the "miniride", so as to avoid hurting the most minimal of rights.

Now I'm sure the whole conversation above seems trite and choppy, but bear with me. My confusion with the whole thing is rather quite simple. Regan states that the miniride principle maintains a sort of "egalitarianism" by making all our rights equal and thus asking for the smallest amounts of rights to be violated. But aha! Therein lies the contradiction and my contest of the idea: wouldn't it be more equal to violate the whole?

If one violates the rights of the whole group, then all rights have truly been considered equally and dealt with accordingly. To violate one or a few persons instead of the whole seems more segregated than anything.

Maybe I have simply misinterpreted Regan, so I ask for comments in any way to discuss or clear the air.