I just don't think there is a spectrum. When we say a game is "less sandboxy" do we mean that (i) the players have less authority over situation or (ii) the players have more authority over backstory or (iii) something else?
It's like saying that cars are on a spectrum of more-or-less car-like: if we say a vehicle is moving away from the car end of the spectrum are we saying that it is more like a truck (ie not really a passenger vehicle), or more like a pedal car (ie not fully reliant on an engine for its motive power), or more like a motorcycle (ie fewer wheels, frame rather than a chassis - I hope that's the right terminology - etc).], or something else.
Cars are in the middle of a spectrum of sorts, which starts with the Terex Titan at one end and moves through road trains, semi-trailers, garbage trucks, 2-tons, 1-tons, vans/pickups, SUVs, large cars, mid-size cars, small cars, mini-cars, closed-cabin 3-wheelers, open-air ATVs, open-air three-wheelers, large motorcycles, small motorcycles, motor scooters, mopeds, electric bicycles, pedal bicycles, one-wheelers, and which probably ends at roller skates.

(and I'll freely admit I probably missed a few stops along that line)
I wonder if you're conflating players making authorial setting decisions with players making campaign-direction decisions within a pre-established or pre-authored setting. It's the latter where the sandbox-to-linear-to-railroad spectrum lies - how much large-scale decision-making the players able (or allowed) to do within a pre-authored setting, be it published or homebrew.
In an absolute sandbox the DM just lays out the setting, sits back, and turns the players loose on it to find/create their own adventures if they can.
In an absolute railroad the players (and PCs) do exactly what the DM tells them to do, no variance allowed and with most if not all outcomes pre-ordained.
There's a clearly-visible spectrum between these two extremes; and that's (I think) what's being talked about here, with it being taken as a given that the whole spectrum assumes DM authorship of setting.
There's also a tangential spectrum, that might or might not cross this one at some point, that looks at how much authorship the players have over the setting with little to no regard for where that campaign sits on the sandbox/railroad line. That seems to be what you're talking about, and it ain't the same thing.
