I'm pretty sure all sorts of public and private institutions get get sued/settle out out of court ever day. Hit by a foul ball, slip and fall in the sugar aisle at Walmart, shot by police, these things lead to costly settlements every day. All of these "victims" should have exercised greater caution but that doesn't mean they don't get paid off.
Case law is not relevant when the cost to fight a frivolous lawsuit and the cost of the bad press is greater than the cost to settle.
You have an uphill battle. Those items you mentioned, the one who caused it was an employee of the place. If the thief were an employee of the hospital, you'd have some recourse against the hospital.
When I worked for a law firm that did insurance defense, my boss would describe the firm as one where if you slip and fall in the store, their job was to make sure you didn't get a dime.