Your challenge will be to prove UA was negligent in handling the bag.
Many companies use disclaimers to say they're not responsible, but that's only true if they exercise reasonable care.
Another example is a parking lot valet. There's always some clause on the ticket about not being responsible for loss or damage. But that doesn't mean they can ram your car into a wall. They must exercise reasonable care while handling your property.
Same goes for UA. They'll throw the book at you, most likely, and you'll have to fight them. But keep your cool and demonstrate that they are at fault because of how they handled the property.