This strikes me as a very complex question and one that would have
different aspect depending on if an institution is funded with private or
with public funds.  Many donors ask their names not become public
knowledge for a number of reasons.  In general, I have thought the public
should have as much information as possible about the objects a museum
holds.  As far as security  concerns, the bad guys pretty much know what
you have already  and I think that a museum would not be eager allow
anyone, including staff who are not directly  working with the collections
in storage areas.