Hello - I see this, thanks.
What happens is that the control point which lies on the symmetry plane is moved across the plane - even though the vertex does not. You can see this if you Tab into box mode.
Ah, that makes sense. Thank you!
I was surprised to see that moving a single point created 2 extra faces.
Everything tries to merge together if you cross the symmetry borderline.
I guess this is not Symmetry but Reflect after all.