Forget what I said before; I found what the problem is.
The way the Iris is modeled is (simplified to the part that matters here) something like this:

Now, if you Scale the Voronoi Texture in Y, that will only affect the inner part, because the outer ‘ring’ is already ‘scaled 0’. I hope that makes sense to you.
This also happens when Kent does this, but the flat outer part is hidden behind the Sclera.