It shows that a low voltage is enough to emit electrons - and the local field near the surface can be very high due to surface effects perhaps.
Uncertain, I agree, but possible?
In my opinion that mechanism is unnecessarily complex and do not entirely explain the effect, since once you have electrons emitted from the surface you still have to ionize the gas, and this requires additional energy. Also, the LEC does not work in vacuum (no current), so the "enhanced" emission of electrons (even in vacuum, where it is easier) can be safely discarded.
By the way, photoelectric effect is able to do something similar, and it is easier to achieve, but you cannot obtain the entire LEC phenomenology just by using photoelectric emission (for the same reasons above).