Wait, what? I work for a software company, and our marketing people (including up to Director level) are some of the least knowledgeable people when it comes to how our software actually works.
Somebody Randi shared it with used the tag (or comment) feature, which then caused it to show up in the feed of Randi's friends-of-friends. Those people had no idea that the image wasn't public (because they don't directly know her), and simply assumed it came through a public feed.
Randi thought that one of her friends somehow shared the image, which wasn't the case at all. They were simply using a common Facebook feature. She clearly misunderstood what was happening. And she acknowledged her misunderstanding by deleting her twitter comments on the matter.
Directly from Zuckerberg's tweet:
""@cschweitz not sure where you got this photo. I posted it on FB. You reposting it to Twitter is way uncool," Randi said in her tweet."
It was reposted to twitter. Randi shared a photo on Facebook. This person was able to see it because she was friends with Randi's sister (friend of friend). The user then took the photo from a semi-private space and shared it publicly on Twitter.
But that is different from knowing how the software actually works, what settings you need to turn on to achieve which result, and being able to explain why it is working the way it is. That is more of an engineering function, and knowing the details inside out is the job of not marketing, but of user education and training.
Maybe you need better marketing people?