I'm not sure what the actual proof of parking pass may be if you were to buy the annual pass online but to show up and pay to park at the actual access point entails putting $5 cash into a lock box. This means that you get no paper proof in return to place in your vehicle to prove that you have paid. I'm not sure if this works on an honor system or a park ranger checks the box often and counts vehicles (I've never seen a ranger at the trail), as that would not be solid proof. I live at the Pulaski trailhead and I have certainly shown up before and discovered that I didn't have cash in hand to place in the box. I may or may not have went for a run regardless, and I am not condoning skipping the parking fees, but I can't imagine paying $5 every time your wife parks in an access lot for 30 minutes several times a day either. That fee should cover a full days worth of parking and that may mean multiple access points as well, you could always contact with questions.
New River Trail State Park
Phone: 276-699-6778
Email: NewRiverTrail@dcr.virginia.gov