In scenario 2, you state that the alarm company can be held liable for the false alarm.  As it turns out, the alarm (hold-up) was a valid alarm, sent by a properly functioning alarm system, which was activated by the 3 year old child of a bank employee. This child was not in the control of the parent which is considered a duty outside the home, and not only did the child have access to the 'hold-up alarm', but also could have faced injury exposed to normal business related equipment which would be considered 'safe' to an adult.
    This was not the first time the child had activated the hold-up alarm. The parent was warned about allowing the child in the bank while out of her control. In addition, no phone call or other notification was made to cancel, or explain the alarm. Someone at the facility at the time each alarm was triggered had to know the account code, password and other info. With no phone call, the police had to treat this as an 'actual hold-up'
    Also, Illinois Statutes require than an emergency vehicle driver operate the vehicle with due regard for others safety. Was it demonstrated the the plaintiff did operate the vehicle in that manner? 
    Can an alarm company be held liable for a properly working alarm system?
    As for the bank, you don't allow children in work areas, with only limited exceptions, and NEVER without direct supervision. It's like allowing circus clowns to hold a party in a stemware shop.
    Please point out where I may be wrong in my interpretation.
    It wasn't my opinion that there should be liability, it was the Court's decision to impose liability.  So the issue becomes, can an alarm company be held liable for damages suffered by third parties [and perhaps subscribers as well] when there is a false alarm even though there would be no liability if it was a "real" alarm?  One wonders why it should make a difference.  One of the many things you learn as a lawyer is that you can't always apply sound reasoning to a legal outcome.  Sometimes the law is what it is and that's it.  I categorize this in that category.  Don't shoot the messenger.
    The reasoning applied is that the injured person should not have been in that situation but for the unnecessary alarm.  The Courts dealing with this issue most likely didn't struggle with the nuances of a false alarm.  Sure the button was pressed and the alarm did exactly what it was supposed to do.  A panic alarm gets no verification; just dispatch, so the alarm company did what it should have done.  But as it turns out the alarm was not a real emergency condition, thus unnecessary from the Court's perspective.  Since I spend most of every working day figuring out how alarm companies can avoid liability I'm probably not the best one to offer justification for the way the Courts imposed liability for false alarms.
    None of the cases we reported on mentioned indemnity.  Hopefully the alarm companies had proper alarm contracts with the subscribers that included indemnity.  Also, the alarm companies should have insurance [probably why they lost the cases].