There's plenty of market manipulation possible even on a fully accredited exchange - e.g. "ramping", "painting the tape", "ghosting" (and all kind of other tricks that were routine in the early days of stock exchanges!). It's hard to know if it market manipulation is happening or not - we just have to trust the "fully accredited" exchange and the regulators to keep the market honest.

One advantage of a P2P exchange with a global order book block chain is that all orders ever placed can be seen by all - making detecting market manipulation much easier.

There may also be differences in incentives - a P2P exchange can be run for the benefit of all, whereas a central exchange is run for its own benefit (and may choose to ignore manipulation as long as it is not too blatant). For example, stock exchanges could use a "discrete double action" system to provide fairer order matching and limit high frequency trading. Why don't they? Perhaps because that would mean less volume and hence less fees ...

On the other hand, when it comes to the "looking after the fiat money" side of things, yes, I would prefer the fully accredited exchange!