Hmm, I'm not sure I follow. On a technical level, a pure p2p system continues to function without central coordination even if each individual node is "owned" by the same entity. These seem to be two very different levels of analysis. If I understand your claim correctly, you are pointing out that this hypothetical entity is centralized -- and I agree -- but that doesn't magically turn the p2p system in question into something else.
To reformulate the question: when is it advantageous for this abstract entity to use a p2p system in this way rather than a client-server system?
Is it e.g. a question of scale?
I have a nagging suspicion that it's partly a question of usage-patterns, though I'm struggling to put my finger on it. This is what I mean by "organizational policy" (which is admittedly an opaque term...)
p2p requires peers, so called for good reason, because their interests and cost/benefits must align sufficiently for them to engage in using the same protocol. thus, "who these people are" dominates the question of control over the network.
tl;dr behavior of users networked by a putatively decentralized protocol will ultimately conform to the social organization of those users, not to the rules of the protocol. these will be routed around or backgrounded as needed to achieve the objectives of the dominant members of the group hierarchy.
the paradox is simply this: decentralization implies the absence of a decentralizer. there can be no "center of decentralization."
I contend that the term is much closer to incantation than implementation in practice.