Although I had a Virginia driver's license back in the Dark Ages, I don't recall anyone asking about medications at that time, but I'm going to take a guess as to why gabapentin (the generic of Neurontin) raised a red flag. Initially, Neurontin (while still under patent) was prescribed as an anti-convulsive medication. It later was used for diabetic neuropathy and postherpetic neuralgia. Common side effects can include sleepiness, dizziness, and in some cases, aggressive behavior.
I can see someone at DMV say/think that the side effects are dangerous for drivers and others on the road, and, if someone has lost the feeling in their feet, their driving abilities can be impaired.
From personal experience, when initially prescribed gabapentin for my chemo-induced neuropathy, even the low dose gave me brain-fog which made me feel unsafe while driving. (One begins on a low dose and works up to a therapeutic dose after a few weeks with this kind of med). I stopped taking it after three days. I then was prescribed venlafaxine. A few days after taking the minimal dose I found myself driving 40-45 mph on the freeway, and it took me several minutes to recognize the inappropriate speed. I immediately stopped using it. So yes… I can see the DMV's point.
Because being able to drive is crucial for me, this is why I went in search of a non-pharmaceutical which could address the pain/burning in my feet and hands.