If this guy's job doesn't require driving, then as a supervisor, it's none of your business. However, if, as Ken said, your company could be held liable for him driving on base, then you need to investigate it.
If his job requires him to drive, even once, for work related business, you should require a driving record check. Anyone can go to motor vehicles and get a licence check on anyone for $5. The person in question doesn't need to be consulted, you just need his licence number. But if you do this and you are wrong or if it really is none of the company's business, you could get in a lot of trouble at work.
As a concerned citizen, it is your business and you should report as much as you know to the authorities. If he's on base at a given time, report it to them.