I would imagine that in most cases the events turn out as you described, Destroyer.
But I think it is possible to have a break up and remain friends, or at least friendly.
It'd rely on a couple of things though.
There would probably need to be a mutual breakup. So, the two people breaking up because it is both in their best interests or they know that their relationship isn't working how they would like.
I don't think there's much chance if the breakup is due to say, an affair, or because one person is abusive or is no longer tolerable.
Both people would probably need to be quite strong in ignoring any feelings for each other, if they still exist. There likely isn't much room in an ex-based friendship for someone to still have longing feelings. Getting back together is more likely to happen in a movie or soap opera. And if one person is still fauning over the other then it's unfair on them to be ignored and for the ex to have to pit up with that person.
I think that if your relationship sprang from a good friendship in the first place, and the above two are true, then it's not impossible for exes to become friends. There might need to be a break between breakup and friendship though, to prevent hostile and conflicting emotions hurting each other.
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