Is this also true of Linux? Or were us humans the stochastic parrots all along?
It is not, nor of open source software in general.
In general, the saying is specifically in reference to services provided over the internet -gmail, youtube, whatever. Note that you don't have the right to modify them and share your own copies -they're closed source.
So no, it's not true of Linux, GNU, etc; it's an apples and oranges comparison.