My understanding is that the NATS/IAA FAB is a fudge. Rather than be forced into it by the EU, NATS/IAA are claiming that their relationship is close enough already to count as a FAB.
As for the 'sector of airspace managed and operated as a single unit' definition - there have been legal changes wherein each provider is responsible for each others airspace, though in practice neither intends to operate in the others airspace any more than they do so already - at least not yet.