"A correctly sized cartridge in a chamber that HAS excessive headspace does exactly the same thing. It stops on the shoulder, then stretches to fill the available chamber."
Not quite. When the chamber is overlong or the cartridge too short, correct firing pin protrusion will not allow the primer to fire unless the case is gripped by the extractor. Then the primer will fire, but the result is the same as a rimmed cartridge, the front simply blows out to fill the available space. It is that condition that can be compensated for in reloading by neck sizing only.
If a short round can fire with the base well ahead of the breech face, there will be case stretching, just as with excess headspace in the rifle.
As to headspace being purely a matter of the gun, that is not really true. The variation in ammunition is the reason why there is tolerance in headspace; if there were no tolerances in ammunition, headspace could be set to a fixed figure which would hold until wear and bolt lug setback changed it. For example, a GO gauge is used to determine that the longest case allowed under ammunition tolerances will chamber and fire. A NO-GO gauge ensures that the shortest case allowable under ammunition specs cannot stretch enough to separate. So there is definitely a relationship between ammunition and headspace.
But chambers don't change or expand (at least not to any measurable extent). What changes are the bolt lugs and lug seats, which compress and wear over time. That results in increasing headspace. When headspace reaches a certain point, it allows the rear of the cartridge to push the breechblock back far enough to cause case separation. If not corrected, the cartridge case will ultimately back far enough out of the chamber that it will have insufficient support and will blow out, wrecking the gun. And no amount of reloading care will change that situation; it will only delude the gun owner that he is "making up" for excess headspace.
Jim