If Apple promised program buyers earlier or priority access to upgrades as part of their deal, then I could perhaps understand the justification.
The carriers' similar payment plans fail in the same way -- just because you have Edge or Next and are eligible to upgrade, doesn't mean you have some form of guarantee -- you get the same priority as anyone else. Whether it should or shouldn't be that way is up for debate, but right now, everyone has the same shot.
In this case, all Apple said was you can get the new iPhone every year. That doesn't mean "on launch day", just that you become eligible to get a new phone every year. I expect the terms of the plan will make this an open-and-shut case.
That said, one thing in the complaint is reasonable, in my eyes -- this whole "come back later" process shouldn't be a thing. Quote them "Backordered" and let them at least order and get in line, instead of waiting a seemingly arbitrary amount of time just to try to get in line later. Apple knows logistics, they should be able to give a ballpark estimate when the Nth device will roll off the line and ship.