I feel like the staff have much less oversight/direct imput than you would expect in a place like this.
They don't seem to have "plug in and pull out" audio/visual access to host memories and interactions, and there have been a few instances that have made me wonder how they don't have more detailed information or absolute control -- "What did your father say to you?", how they seemed unaware of the fly triggering the sheriff's bug, how they didn't shut broken homicidal milk maniac down immediately, their opaque knowledge of what's happening inside Thandie Newton, etc. It feels more like they're maintaining balance in an ecosystem than directly managing events. On a general basis, that is, when they don't have to orchestrate a 200 host recall.
Anyway, the privacy stuff makes sense, since I doubt guests would want anyone monitoring them too closely, and it makes me lean away from staff speaking through the girl. They seem to operate more general, "If it ain't broke, don't interfere" policy. The handlers were trying to get the MiB to stop because he was potentially disrupting the narrative via mass slaughter, but I don't think they're aware of the "game" he's playing, which I'd venture to say is against the interests of the park as a whole.
That doesn't explain how the little girl said what she said, but I feel like she's the one who said it. Maybe part of the "deeper level" of the game he keeps talking about is how to work the right hosts in the right way to get them to break character. After all, he knows the sort of horrors these hosts incur on a daily basis without breaking, but he persists. He must be doing something different to believe that he'll get different results, otherwise he wouldn't be doing it.