I work in a hospital, and I've heard a total of 3 political discussions. One took place in my office, one in our shop, and one in the hallway nearby...all places far from patients, family or visitors. I have never, ever, in all my working around the rest of the building, heard staff having a loud political discussion. Ever. If people want to discuss things, they go in their lounge or break room - and every department has one.
Now, she may well have overheard a discussion, but I'd bet anything that it wasn't medical personnel speaking. We have no control over the discussions of visitors and family...and no intention of trying to obtain control.