To give some more pushback on this assertion... I've been developing software for 21 years now, and the only positions I had where there was negligible open-source software were in the first couple of years (in the automotive firmware space [OnStar], and a brief stint in some defense contracting). For the last 18-ish years--firmware, systems, enterprise, virtualization, demos, security--everything I've worked on has largely been based on open-source software, or the product was open-source itself. What I've never done professionally: Web app development.
Honestly, I think it would be hard to overstate the prevalence and impact of open-source software in the field of programming (and really, the entire tech field).