When you share something on the internet, you are relinquishing control of it. Someone can always manually redistribute content you create (for instance, saving a photo you share with them). As such, you should never put content on the internet you never want being made public.
Unintentional sharing on facebook is solely caused by its horrendous interface. The interface makes it too hard to precisely determine what is being shared to whom. Given that cognitive faculties and time are limited resources, the average user will not have time to decipher facebook's sharing settings. The result is they have a high likelihood of unintentionally sharing information, resulting in privacy concerns.
In real life, if I tell something to a trusted former high school friend living in a different state, I can assume at over 98% confidence that my boss at work will never know the content of the conversation. They are two completely distinct social circles, or groups of friends. The channel of communication is different for different groups of friends. This is how real life works.
People expect a well designed website to work in the same way.
But because each is separate and you can communicate freely within each group and not worry that it might accidentally get shared to another group you start to see more meaningful engagement.
Now no one can prevent someone from taking a screen shot and sending it out but like hosting a house party you trust that your guests won't be jumping on your furniture or tearing down the wallpaper (unless it is that kind of party...)
But most people don't because it's challenging enough. The idea of these startups isn't to achieve perfection as much as to make it a little more safer for you to share stuff.