I think this is all quite new to most museums, and while it's clearly an idea whose time has come, they don't really know what to think about it yet. Copyright is only an issue for relatively recent works of art. Anything over 100 years old (or so, depending on when the original artist died), not to mention fossils or other natural objects, has no copyright protection. But that doesn't mean that a museum might not want to maintain exclusive control over the distribution of any data that would enable reproductions to be made from items in their collections.
This may be opening up, slowly. I haven't seen any major collections freely sharing STL files of their collections yet, although some, like the Smithsonian, have launched into ambitious scanning projects. But in the hope that they might find this a potential source of revenue, I've started a site where those with collections of scans can offer them for sale: 3Dscanhub.com
I just launched it recently, seeded with scans I've made myself of fossils, natural objects, antiques, sculptures and people (or parts of them), but the idea is to invite other individuals and institutions to offer their 3Dscans for sale, and hopefully create a market for stock scans. If anyone here has high-quality scans which they're authorized to distribute that they'd like to try selling, please get in touch.
Andrew Werby
www.3dscanhub.com