The blurring of the line between "in your own home" and "on the Internet" is the crux of the issue. The average person doesn't understand that bringing Internet-connected devices into their home makes some quantity of "behavior in their home" into "behavior on the Internet".
Application developers are deliberately trying to blur the line, too, in their user interface. How many users really grok that when they use iCloud syncing with their photos, they are uploading their photos to the Internet?
Since many of us grew up before and then after the Internet, we kind of instinctively get what application functionality needs the Internet, what functionality doesn't, what gets written to the Internet, what gets read from the Internet and so on. Younger computer/phone users don't get this at all. My 11 year old has no mental picture of why X requires Internet and Y doesn't require Internet. She doesn't understand the concept of Data A is stored on-device, and Data B is stored on the Internet. And honestly, I'm even having a harder and harder time explaining it. Tech applications have totally blurred and grayed the previously black-and-white line.