However, it's possible that at sufficiently high voltage the juice could arc past the air gap.
That's right, although the dielectric breakdown voltage for air is approximately 3000 V/mm (= 3 kV/mm), but it can depend on other factors such as the geometry of the gap and the air pressure. Generally, however, it's unlikely that anything less than 1000v would bridge that gap. Much more likely, given the first recorded instance was of a drunkard whose coordination would also be somewhat suspect, is that the unfortunate individual in question touched the rail by some other means, albeit fleetingly. That could easily tip him into more direct contact. As to the others, would any sane and sober individual ever get close to a third rail?