I haven't tried to find the actual flight path, but for a transport aircraft at cruise the "closest airport" would not be underneath the flight's position, but rather at some distance away corresponding to the computed distance to reach the surface in an idle power descent.¹
From 30,000+ feet I'd expect that value to lie around 60–80 miles, iirc.
/Acey
¹–ignoring in-flight fires, medical emergencies, etc., that might dictate an unusually steep descent profile.