Without knowing the exact circumstances it's tough to tell. But considering that a wide variety of experiences and mistakes make up the population of folks working at every company out there, no single incident is an automatic disqualifier unless it was obvious and willful negligence. (And even then some companies have show leniency).

"Past problems" covers a lot of territory. I know a fewl folks who work at various national/legacy/major airlines that have had violations, including one that was an ADIZ/Restricted Airspace suspension.

Attitude will dictate a lot. Assuming that this individual checked the appropriate boxes on the application, the company is at least willing to hear their side of the story.