I am sure it is assembled right and consistent with photos. And the floating swivel behavior of the linkages works too. I have seen it swivel while ferrying the mower around and it can be done by hand by pushing/pulling on the yoke when the mower is not mounted on the tractor. The various pins are bolts with bushings to allow this behavior.
Unfortunately, it seems to have been an afterthought or not properly planned into the design. They really needed to put the vertical angle iron posts a bit closer together if they were going to bolt the top yoke piece to the outside and push the pins farther apart. Or use a different type of post that would allow reversed pins to work and allow swiveling with the pins reversed.
I can't believe the manual suggests reversing the pins as a solution to this problem. That would hide 60% of the pin behind the angle iron and not leave enough exposed pin to be of any use.
My best approach now is to look for longer pins that can be reversed, but make sure that doesn't put too much bending leverage on the posts. I could weld a tab or ear onto the posts to alleviate that, and it wouldn't compromise anything.
Because of the angle iron, using longer reversed pins will take me from being 1-2" wider than cat 1, to 3-4" narrower than cat 1. Stupid.