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My Royal H has a modern TA crankset I ran it with a 107 Shimano BB for a few years, I tried it on another bike with much larger chainstays and the the ND side hit the chainstay. When I went to reinstall them on the Royal H I installed them with and 111 Centaur BB and it fits the same.
I also ran a GPM strada cranks on a Shimano BB for about 7 years.
So yeah, I’m not so convinced it’s a myth.
Eeyorecore-
I installed them with and 111 Centaur BB and it fits the same
That's already half the error you originally claimed, and just 1mm different from what I would predict if you asked me to guess at a starting point for substituting JIS for ISO.
If you look at all the potential sources of axial displacement error at the pedal end of the crank which are generated by the boss/spindle taper interface, you'll quickly realise that you can tell nothing about the "standards" from assembling one crank on two BBs, especially if you are just eye-balling it rather than taking proper measurements with the cranks in all 4 possible orientations on the spindle and with consistent bolt tension. How precise is your torque wrench?
If you wan't to reverse-engineer the standards, you should probably take at least 10 samples each from 10 manufacturers (5 JIS, 5 ISO) into whichever room your CMM is kept in, but my previous advice stands: check every individual installation for correct fit, because wear and tolerance stack happens. Either that or ditch the stupid things and get some cranks with a proper spindle attachment.
gbj_tester
This is a myth. People assume that because it was on Sheldon Brown, it must be true. It's a pity he didn't live to correct this, because it gets rolled out as fact every time the subject is discussed on any cycling forum, and asserted as an absolute fact by people who have clearly never measured a pile of square taper bottom bracket spindles to see what the difference really is.
Regardless of any JIS/ISO confusion, you should always carefully inspect any square taper assembly, even one which is supposed to be a proper match from the same factory, to ensure that the bolt head doesn't touch the end of the spindle and the crank doesn't touch the runout of the taper at the big end.