I'm a little disappointed that the article's author didn't make a counter-claim, or at least speculate on what some other reasons may have been.
I'll throw my idea in: most spiral staircases turn counter-clockwise, because they were notoriously dark / badly lit, so one had to hold a torch or a lamp while traversing them. Since majority of people are right-handed, stands to reason a person would be holding the source of light in their right hand, and hold on to the hand-rail (or wall) with their left. You'd naturally want to lean on the outside wall of the staircase, as the stair treads there are wider than near the centre of the spiral.
The flaw is whatever x-wise you pick, you have the torch in the "wrong" hand either going up or coming down. Also, hand rails weren't a thing in most medieval staircases; you were expected to just not fall, and when you did there was no one to sue.
If I visualize walking up a staircase, I'd much prefer them clockwise so that I can touch the center with my right hand when walking up, for some additional stability.
Also, much staircases I know are clockwise. Which is also my theory for this myth, most staircases were build clockwise simply because most were already build clockwise. It fits Okkam's razor.
The stair is much thinner near the center though. If the center pillar was wide enough that would probably be fine but if the pillar isn't fairly large your foot may only get like an inch or two of tread near the center and be easier to fall down.
I'll throw my idea in: most spiral staircases turn counter-clockwise, because they were notoriously dark / badly lit, so one had to hold a torch or a lamp while traversing them. Since majority of people are right-handed, stands to reason a person would be holding the source of light in their right hand, and hold on to the hand-rail (or wall) with their left. You'd naturally want to lean on the outside wall of the staircase, as the stair treads there are wider than near the centre of the spiral.
QED!
(let me know if you spot the flaw in my logic)