"What matters is the intent."
"A desktop PC running kiosk software *does not*."
I think you are over generalizing again. I know of quite some Kiosk PCs which are installed, configured and updated by their respective owners or their employees and have not been rendered unmodifiable (neither technically nor legally) by the device's manufacturer.
Just like with embedded devices, the device category does not imply the availability or absence of customizability.
Some systems detect updates on a server (or even boot through from server), some require remote access (e.g. SSH), some can be updated through a physically connected media, some need swapping of their system drive, some need to be powered down, connected to an updater device and reprogrammed through that.
Since you like general statements so much I'd say that the majority of systems is designed that way and only a very small portion has been artifically restricted by technical (e.g. cryptography) or legal (e.g. renting instead of selling) measures.
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