I did some calculations on this because... well because I care about things a little more than some and am intrigued by the answers I get.
The 8 frame langstroth box is not a Langstroth invention, but rather a later modification to the existing standard 10 frame box. The original, if I am not mistaken was based off of a peach box or some other readily available shipping container of the time (reduce, reuse, recycle!). That being said, I believe the early calculations suggested one size width for frames in the brood nest and a different one (wider) in the honey supers. The 1 3/8" current size is a compromise between the two of them.
There are some calculations that involve average length of a chrysalis, the thorax size of a bee, and so forth that suggest the optimal distance between frames on center, and I believe that is where Michael Bush gets his 32 mm (1 1/4") from. Though I do wonder, since I know that he goes more towards using "small cell" or actually "natural cell" sizing he would have smaller bees. I am not sure this would affect that 32 mm number if one were still using industrial sized cells.
In addition, as I mentioned earlier, the 8 Frame modification was one of the mfgs (can't come up with it now) and the internal size left more room after the number of frames were added up than the 10 by a whole 1/4". So when you add together 10 frames at 1 3/8 then add exactly 1" you get the interior width of a 10 frame box. If you do the same with an 8 you have to add 1 1/4. Granted you need some space, otherwise you would never get the frames out without rolling a bunch of bees. But, why the difference? I wish I could remember who told me this, but the reason given was to accommodate an internal frame feeder without having to remove more than one frame.
Perhaps that is true, or perhaps apocryphal.... but you now know what I know :)