Lead Balloon, a Part 142 certificate holder only has one Head of Operations. Duties can be devolved, but not responsibilities, so you could have a Senior Base Instructor or similar who might handle the day to day operations at a remote base, but the HOO of the whole structure will certainly have the ability to ground a 'rogue instructor'. There cannot be a rogue CFI, because the HOO is what we used to know as a CFI, and that person sits at the top of the operational structure of the organisation as a whole. This will all be laid down in the exposition in detail.
If I'm telling you how to suck eggs please let me know and I'll stop, but I stress that the operation works by the procedures in the exposition, which must include how flights are authorised, how instructors are checked and supervised, and how that all ultimately flows down from the HOO. If a multi-layer organisation has an exposition accepted by CASA (as it must to operate), then that becomes the legal document with which it and its personnel must comply. If the HOO finds out someone in the operational structure isn't doing the right thing, he or she absolutely can stop that person flying.
I don't know what you're envisioning, but the HOO would be in breach of his or her responsibilities if systems weren't in place to stay informed about what was going on at remote bases and to ensure standards were being met. Of course, systems are only any good if they're used properly, but someone's only going to be able to 'go rogue' if they're left alone without proper supervision. I'd hazard a guess that robust systems would have been specified in the APTA manual suite, and would have been working effectively too. This is where the HOO's operational control lies, not in the financial or other arrangements between the parent and subordinate entities.