Assuming the back strip was the same thickness as the back, then the reinforced section would be twice as thick as the rest of the back, meaning the reinforced section would be twice as strong as the rest of the back. The grain of the reinforcing strip is rarely going to be exactly parallel to the back or the seam between the back pieces (any runoff to the side or waviness will make them nonparallel), so there likely isn't going to be the weakness that you're postulating). It seems to me that the area of the center strip is likely to be twice as strong as any other part of the back, even with the grain going in the same direction, and any cracks are likely to happen elsewhere. The center strip perhaps comes from a history of glue joint failures at the back seam, due to the very limited surface area and difficultly in clamping the joint with much pressure. The center strip increases glue area by 25x (or whatever) and is easy to clamp. If you're just preventing a glue joint failure at the seam, grain direction doesn't matter. But it might matter eventually if the center strip glue fails due to seasonal movement.
Of course, I'm not an expert and I could be wrong about this. If anyone has examined a number of cracked instrument backs and found the center is where they tend to crack, that would be good information. I have heard that backs tend to crack beyond the ends of the cross braces (if they're not run all the way to the sides), so it may be that the cross braces are really what are preventing cracks, and the center strip grain orientation may not be that significant.
