Cherry's engineers are deliberately trying to screw with me. I made the square stem design I made the same size as the cylinder that is normally used. That is, the diameter of the cylinder was used as the width of the square stem. One should expect it to fit into the hole then, yes?
See that little notch in the housing above the stem in this picture. It allows for a cylindrical fitting of a cap to pass into the hole even though the fitting is larger than the stem. If you ask me, it looks like the entire key was designed and ready when they realized, oh crap, there is too little space for the stem attachment of the cap and then they added that small feature afterwards.
Ni biggie, but it means I have to decrease the size of the stem fitting a bit.