Not to belabor the point, but don't you think coordinating the object in the frame IS arranging them somehow.
Lets say you as a good photographer walked upon a scene you would do a better job, with lens choice, lighting and picking which things to include in the frame and how to show them ( depth of field, angle, contrast etc), than someone with no talent that just walks up and tries to take a picture of something.
Isn't that what photography is all about. Isn't that why 10,000 Ansel wanna-bees keep looking for his tripod holes in Yosemite.
How often do we get asked by amateurs to critique their work and we tell them, your composition is a bit off, the lens choice could have been better, you should have cropped more.
Personally I think we do a lot of arranging and coordinating the objects in a picture.
I coordinate peoples bodies in ways that shows them in more flattering ways. I choose what to include. I choose what to accentuate and what to hide. I choose how the background and foreground play into the portrait. I can't change their face but I can perfect it with light and angles.
Anyway I think we do a lot of manipulating of the elements that are in front of us.
Aren't you mixing up staged photography with unstaged and we presume HCB's was all unstaged, thus coordinated and not manipulated. Or are we starting to split more hairs.