Slowman - Stack and Reach question

For some perverse reason I have a desire to understand this stack and reach theory. What confuses me is the proposition that seat angle is irrelevant.

It seems to me that I would need to specify a seat angle first in order to be fitted using this terminology. If I decide that 77 degrees is best for me instead of 78 would I not need a shorter “reach” to compensate for my hips being further back? If I try to keep my saddle the same distance from the BB at the new angle, it seems that “rotating” my FIST-perfect position around the BB would also call for a slightly higher “stack”.

Dan talks about points in space. If I imagine a perfectly positioned rider without a bike I can fix one point, the feet, relative to the BB and then rotate the picture to come up with infinite combinations of stack and reach, all of which would be determined by the seat angle. I know I’m missing something here, but what?

Bump, per Dan’s email.