There is an inverse relationship between the rumor mill and intentional information flow from management. If you are not giving your people good information to make decisions, they will find other ways to inform themselves. This means they will rely on rumor and innuendo to fill in the blanks.
I worked at an organization where one of the directors was terminated suddenly. Even though I was on the management team, I was given no explanation. I started to ask questions about what had happened to this gentleman. The stories I heard were of lascivious affairs and misconduct. Whether or not that was true, I still don't know.
If you want people to make good decisions then provide them with as much information as possible. If you feel like your people can't be trusted with sensitive data then you have the wrong people working for you. And their imaginations are always worse than anything you can tell them.
What is stronger in you company, the rumor mill or factual information flow?