First, I don't think its going to make a big difference either way because with the multiple support points the battens aren't under a great bending stress.
I've often seen things that puzzle me and I wonder why someone did something a certain way. I then try to do it my way, and I quickly learn why they did it their way.
This arrangement strikes me as one of those things.
So, what would be the functional difference if all bolts were parallel? The first thing that comes to my mind is that the arrangement would resist bending in one direction better than another. The "crossed" arrangement provides equal stiffness in all directions, which then makes the orientation of the batten itself unimportant.