It's actually the opposite (to a point, I think). Higher mean free path means more time to accelerate, then hit and ionize something else. That's how fluorescent tubes maintain discharge a meter long at measly voltages.

Radiation doesn't help either, as sibling commented - it creates ions making the initial breakdown easier, though it shouldn't make a difference for a continuous flow that involves innumerable ions.

Here ya go:

https://www.youtube.com/watch?v=MIqK45nxcTo

He even explained it with balls and magnets!

I would guess that it could be due to having more ions in air due to higher radiation levels.