Most hospitals have this policy. Not so much like a school's gun free zone, where they're all afraid of someone coming in for a mass murder, but more for the off duty cop who came rushing in because his daughter was in an accident, doctor can't save her and he decides to off the doctor. At the hospital I work at our security will make anyone not in a police uniform go back out to their car and secure their weapon. Emotions run high and you're on private property with private rules. Also get problems with situations like when a father is divorced and the wife gets drunk, crashes the car and kills the child in the car seat. That father who's been fighting for custody for the last two years... he's not thinking straight.
There's actually a ton of doctors, nurses and staff who petition to get the policy changed to allow staff to carry for situations like this, but then the insurance companies (liability) step up to the plate to shoot that down.