There are systems consisting of wholly free software, and in some cases the hardware is also driven by free software.
What about mice? Do mice have software on them which would make them "nonfree"? I've plugged this mouse into Ubuntu, Debian and Trisquel Linux distributions and was never prompted to install any nonfree software, which leads me to assume that mice are generic and just send keycodes to the computer.
Computer Mice seem like trivial devices. But I do own a more sophisticated mouse which can be loaded up with macros, so it doesn't seem like mice are necessarily so trivial, and the software driving those macros is probably nonfree. Would using either of these mice exempt me from running a "wholly free system"? (Or would the supposed triviality of such software--perhaps it is unable to make network requests, for instance--make it a non-issue?)