You are pretty much correct. There are different levels of criminal record checks. I'll call them administrative and criminal justice as different jurisdictions call them different things.
Administrative is done by many prospective employers. If you've had an expungement you can say no and your employer gets shown a clean slate.
A criminal justice inquiry is different. It's available only to and use by law enforcement and courts. Expungements may or may not show up on a criminal justice query. They apparently do in NJ.
I'm guessing at the time line but it appears after his convictions for his disorderly persons offenses he managed to get in some branch of the military. He's lucky he did as those offenses will usually serve as a bar to enlistment.
He still didn't clean up his act after the military. He got arrested for eluding and pulling a knife on the police. He's lucky he didn't get shot. Bringing a knife to a gunfight? These are both felony level charges. He pled guilty. This could very well be the reason he wasn't hired by the police department. A good choice by the chief IMO, expungement or no expungement.
He's also playing the veteran's card. Being a veteran myself I can say this. The military is like anywhere else. There are scummy people everywhere with and without criminal records.
I have no sympathy for this guy. We all were young and stupid at one time. Few of us ever pulled a knife on a cop.