You're right. It is mirrored. And you can't do that with an actual sign. You can do that with images. But other words in image aren't reversed. Composite is a logical deduction.
Here's a much larger image I found, but still very out-of-focus in that area.
So we have some form of proof that at least that sign probably can't exist as it's shown in a real hospital, OR the picture is blending 2 or more scenes together and didn't stay consistent on having all text read properly. Maybe Italian backdrop [mirrored] and English-speaking scene closer to the front.