Yes, they got things wrong. This is how any person well-versed in a niche field feels when a mass-market publication covers something which they are personally well-educated in.
There are, largely, two different reactions to make here: pointing at laughing at those dumb Fox Business bimbos who just don't get what we do, and reaching out and trying to help, trying to clarify.
I mean comon.... all they would have had to do was email IT and ask what GitHub does. Surely someone there could have made a layman's explanation for the news that didn't involve the phrase "reciprocity or a big chunk of software."
I personally encountered this issue when explaining Fork the Cookbook to people. But what made this video cringeworthy is the total lack of research the journos seem to have put in.
Question to friend: You have an idea that computer software is written with code?
[Typical person who has used a computer will respond with something like, Yes, I've heard of computer code.]
Follow-up: Open Source is what we call sharing your computer code with anyone for free. Generally, nowadays, programmers can put their code online for other people to play around with.
Sure, there's more to it than that, but that will give a non-technical person an idea of what you're talking about, and probably makes more sense than what Fox presented. All they needed to add for Github is that it's a company which makes this code sharing easier and more organized and there is business opportunity in making software development easier.
Why put up a box with terms if you're not willing in the slightest to get them right? Probably just to to keep up the impression of actual journalism - you're not doing journalism, your viewers don't really care anyway, but they kind of feel informed and you found a really cheap way to fill another 10 minutes of screen time.
(I notice the op changed the title, so this now probably makes little sense.)