When an agency says "on duty" 24/7, they must define that thoroughly because this could cause serious liability and financial consequences for them as well as the provider.
LEOs are given strict guidelines as to what they can do and in what instances they declare themselves to be a LEO for resolving situations while off duty. This definitely includes their carry of weapons off duty and safety within their homes.
If you stop for an accident off duty, are you capable of being financially compensated for your time as being "on call"?
If doing something "heroic" off-duty in such a way that it violates a company policy, then there may be just cause for them not to provide compensation.
A dead rescuer is usually useless unless the body floats and the other victims can use it as a floatation device.
This was discussed in this thread concerning the Florida Paramedics that did not go into a retention pond because they were not equipped to do so. They still have guidelines for their own safety on duty. The same commonsense and/or logic should be applied off duty.
http://www.emtlife.com/showthread.php?t=6185
I can still act as a concerned citizen and do what I can as a private citizen for moral and ethical reasons without asserting a professional relationship with my employer. If my employer wants me to be available 24/7, then how are they going to prepare me with the proper equipment, medical oversight, insurance (malpractice) and monetary compensation? If you are considered "on duty 24/7" and if you screw up a patient outside of work, can you rely on the Good Samaritain law which can extend to off duty EMS providers in many states that help with good intentions understanding their off duty limitations and responsibilities? Or, has your employer outlined how far they will accept liability for your actions?
It is understood with any medical/rescue/fire profession that if there is a major emergency such as flood, fire, hurricane, plane crash or earthquake, you are subject to call back but that is usually in writing with guidelines pertaining to and exemptions of local, state and Federal statutes clarified. This should be in all disaster plans in every EMS agency, FD and hospital.