Why would all of these systems be connected to a single ai? I feel like you are describing something criminal humans do through social engineering, how do you foresee this AI finding itself in this position?
because someone decides to connect them either unintentionally, or intentionally for personal gain, or, more likely, for corporate purposes which seem "reasonable" or "profitable" at the time, but the unintended consequences were not thought through.
Look at that recent article linked to HN about how MSFT allowed a huge security flaw in AD for years in order to not "rock the boat" and gain a large government contract. AI will be no different.