You just caught wind from a reliable employee that another staffer is badmouthing you behind your back.. You don't like confrontations, so you decide to make a general announcement at the next staff meeting that you're aware "some people have issues" with you, and that you expect they bring them to your attention, not everyone else's. You insist it won't be tolerated.
What's wrong with this approach? For starters, you just tolerated it. You just told your staff that someone is badmouthing you, and they aren't being disciplined. Instead, you put the entire group, loyalists included, on notice. You took the "sprinkler" approach hoping the guilty party would feel the wettest. Maybe he/she does, but you've also dampened the spirits of those who don't deserve the blanket accusation.
When you have the facts, the sprinkler approach is the worst approach. It's telling your team you feel they are all capable of holding you in contempt when they're not. Casting aspersions to the entire team for one person's transgression demeans your top performers, demoralizes your champions, and weakens your ability to lead. (Who wants to be led by someone who thinks they're capable of malfeasance?)
When you are certain of the fact, but not the offending party, the sprinkler may be the default approach. But when you have the facts and verified the guilty, get out the hose and douse soundly. Soak the offender and no one else with your written policy, your intolerance of deviations, and your expectation of future compliance with consequences for failure.
Then give him/her a towel and help with the drying. The empowered healthcare manager is foremost a servant.