My school is preventing devices from connecting to personal wireless APs. HOW??

Recently our school implemented some sort of Cisco enterprise service to provide a "better internet experience" to students. (I apologise for the ambiguity - this is not the question though). All WiFi routers are Cisco made, and a monitoring system is also in place to track traffic, bandwidth, etc

HOWEVER, they also blocked the use of personal routers connected to the school's ethernet ports; which is currently messing up my understanding of how such devices work.

The situation is:

1:

When attempting to connect to a personal router which is connected to the school net, a "password wrong" popup appears, as well as a warning (Android): "NETWORK_SELECTION_TEMPORARILY_DISABLED".

On Windows 10 devices the AP will become "connected" for around 8-10 seconds which then automatically disconnects.

2:

Resetting the router to its factory state (resetting to 'OPEN' auth instead of WPA2) will just throw the same error (Android), without the password popup. Same on Windows.

3:

Resetting the router while the ethernet cable connecting to the school is removed also results in the above situation. No inputs or data were transferred from the school to the router, but still the problem.

Now how is this EVEN POSSIBLE?? Is the school modifying the router's internals? A factory reset will reload the router's READ ONLY firmware - But even this doesn't fix the issue! Surly the ROM cannot be modified... My only guess is the school's own APs are interfering/preventing the 'other' APs - Which I doubt is even possible with current tech.

Can anybody please give some explanations pr at least guesses? I'll happily provide more information when required.