Free Software sure, that wasn't the point.
Open Source, that was exactly the point. Eric S Raymond, one of the original promoters of the concept of Open Source coined Linus' Law:
Given enough eyeballs, all bugs are shallow
Which definitely points in the direction of receiving bug reports and patches from users of the application. He was also a proponent of the Bazaar model, where software is developed in public, as opposed to the Cathedral model where software is only released in milestones (he used GCC and Emacs as examples, which reinforces the part of your statement about the Free Software movement in particular).