When someone shares content with you on a closed (path) or semi-closed (instagram) network, is it appropriate for you to take their content and share it outside those networks? Is it the equivalent of taking someone's secrets and yelling them out to the world?

Interesting question - I think that's an implied cultural norm, a way of respecting the virtual walls people feel protected by when they share something within a closed network. That said, it happens so often that "cultural norm" has to be seen as a respected, but not enforceable, custom.