If the employees in your department are being given inaccurate information on any issue or development that could affect their attitude, performance, or productivity, you should give them the facts. The same criteria certainly apply here.
You should meet with the employee who led the discussion, but give him the facts, rather than a reprimand. As for your eavesdropping concern, you are entitled to walk through your department, as this is a normal part of managing by wandering around. In fact, part of your job as a manager is to use all of your senses to try to fully understand what may be happening in the department. If you happen to see, hear, touch, or smell something that is not right, it is part of your job to deal with it.
You should finish your meeting with this employee on a positive note, but before you wrap it up, let him know that gossiping is very counterproductive and there can be severe repercussions for employees who trade in it. And, that's not gossip, that's a fact.
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