Mac,
I have regulated doubles and fully appreciate that bullets don't cross with correct regulation and load.
That was not what my post was about.
Really what I was asking is, where did the belief originate that says a correctly regulated double should print its individual groups apart by the same distance as the bore spacing?
So the question is, why does the distance between the groups have to be the same distance as the spacing between the bores to achieve parallel bullet paths?

Also my question is asking, where is this written as fact?
Have prominent double gunmakers ever stated this, or is it just a theory born on the internet?