The first sign that the Offices of Interchange have different relationships with governments in both worlds is when we see that the alternate ("Prime") Earth integrates OI personnel to a greater degree within the official police forces, while in the normal ("Alpha") Earth, OI agents operate much more covertly and try to avoid exposure to official law enforcement.
The Interface rooms are implied to be a divide between the worlds, and this is later made explicit. Yet, with all the hullabaloo about closing the Crossing, there's never any attempt to secure the Interface Department, nor is there any in-story explanation as to that "Crossing"'s origins. This is especially egregious because the size of Interface's "Crossing" must be far larger than the official Crossing.
It's very convenient for the School that the counterparts of several people they recruited as orphaned children coincidentally grew up to have jobs in the Office of Interchange.
It stretches disbelief that the School could have eyes on the daughter of a senior OI official, including bugs and recordings, from childhood to adulthood without any security or intelligence personnel on our side noticing them.
