Surely the people who speak of "linux on the desktop" (not me, for the record) are at least in some small sense alluding to being able to have some of the freedoms historically associated with Linux, originating in the GNU movement and all that? The right to study, share, etc.
What I mean is that I would have picked Android as quite a good example of how the technicality of running the Linux kernel under the hood means very little in terms of users being empowered, or anything of the sort.