Mickey and Mac,
I must admit that I really don't like this notion that suggests that the bullet paths must be parallel if they hit a 50 yard target at precisely the same distance apart as the bore spacing measurement.
Nor do I like the notion that if they hit a 50 yard target any closer than the bore spacing measurement, that they must be crossing.

I fail to see why the bore spacing measurement has anything to do with the distance between the two parallel bullet paths.

Can anyone show some sort of evidence as to why, in a so called perfectly regulated double, the bore spacing, and the bullet paths, must share identical measurements?

For me, the way to test how close to parallel the bullet paths truely are, is to shoot the double at various distances, starting at about 20 yards and then trying at 50, 100 and 200 yards.
This will soon let you know whether the groups are close to parallel, crossing or shooting apart.