One thing that a hospital needs is an interaction policy that helps employeed decide what to do when confronted with comfusing situations on social media.
Part of a good social media channel, especially with so many employees who have high importance high intellectual jobs like a hopital could benefit from a distributed network of influencers.
While this article deals with personal branding for career advancement, if a hospital were to create a situation where many of it's physicians and nurses were seen as leaders and desirable employees, it would elevate the brand as a whole and even make the brand more attractive and able to retain people.