I think that once you make then decision to use another companies chat system, you have to recognize that just about any information might end up on it.

I can't imagine trying to educate users (outside of an environment in which this thinking is normal) about what can and cannot go over which medium.

The realtime(ish) notifications and questions that they describe in the blog post seem relatively benign compared to say, product planning discussions.

Disclaimer: I used to work at Dropbox and know the individuals involved

Netflix uses another companies infrastructure (AWS), and I'd suspect another company for source control.

Most of the world is doing this now. It's cheaper, easier and in most cases more secure.

That was my concern too. What are the security aspects behind it?

Everyone uses Gmail & Hangouts, and no one bats an eye.