So what does being POST certified really mean in this case? It means the officers have gone through and have been certified. However that may not mean they have any particular authority. Such as for arrest, etc. So the real question is what authority has been given to the Chicago Department of Aviation. So for all intents and purposes they could be considered to be nothing more than "security" officers which is exactly how they are classified:
https://chicago.taleo.net/careersect....ftl?job=99860
That said, I find this bit interesting:
Arrests and detains individuals found violating or suspected of violating city, state and federal laws, restraining individuals using handcuffs or other restraining devices
Which if that is the case, in the UA incident I would think discussing the IDB issue under terms of arrest for trespassing might have persuaded the PAX to be bit more cooperative. (Not saying that was the best course of action but that was the path UA took).