To clarify, because the original article doesn't really mention this: the photos that were uploaded to Wikimedia Commons were taken by a photographer hired by the museum, not Commons users. The museum is claiming that they hold copyright over the photos because even though the original artwork is in the public domain, the photo taken of it has its own copyright, held by the museum's photographer (and thus the museum).
The Mona Lisa is in the public domain. You can include an image of it in whatever you are creating without asking anyones permission. However, lets say you take a picture of the Mona Lisa. That image is not in the public domain, and it is your image and you can prevent people from using your image without consent.
Does this merely mean that if I take a photo of something in the public domain, I hold the copyright on that particular reproduction?
Or that if a museum takes a photo of something in the public domain, they can restrict others from offering/using their own photos of that work?