Well I happen to know a little about Sentara. Don't ask, I'm not telling.
As a private corporation, they are entitled to have their rules, for employees and property. Their security is also unarmed. Not sure if they get background checked.
I would be extremely reluctant to hand over a firearm to private unarmed security.
OTOH I think if you get caught you can count on being asked to leave first rather than having the LEOs called on you, so there is a safety margin before getting arrested.
I am glad that postcard was sent. As anal as they are about being right, they might just change that sign to one that is not incorrect. I liken them to a kinder, gentler form of Nazi Germany. All the germanic efficiency and order without that pesky racism. But there is a hint of world health care domination.
Good luck getting that policy changed.
Oh, remember a few months ago, there was a shooting (or two) in their parking lot. I wonder if all the other facilities are being posted?