I'm all for employees not blabbing company secrets, but employers should definitely give their workers the same consideration.
Having said that, sometimes it's hard to know what is considered sharing company secrets and what's not. A couple of years ago, there was a local online political chat room where someone was talking in detail about what was going on in the newsroom of a local newspaper. I have a friend who works for the paper and she said the bosses were not happy about the talk. They kind of put the word out that if the person got caught, that their job would be on the line. She said there wasn't a confidentiality agreement in place, but that the person saying those things at least should have known better.