I think that's right, companies may have figured out that a decent percentage of people who have a valid right to make a claim against them will simply give up

I think that's right, companies may have figured out that a decent percentage of people who have a valid right to make a claim against them will simply give up and go away when they see such a notice. Signs or a disclaimer in a contract are cheap to add and scale well. An example many people are familiar with are parking lots which display signs with 'We accept no liability...' or similar language. I had my car parked at a hotel in a direct line of sight and close to the front desk and it was vandalised by two men attempting to steal it. They had the hood up, trying to defeat the security system and were trying to saw through the steering wheel to remove a 'Club' steering lock for over an hour while I slept. All of this plus bored front desk attendants on CCTV. I woke up to find this in the morning and asked the hotel about it. They acknowledged seeing what happened and admitted doing nothing. This was a nice car at a luxury hotel, too! I informed the manager they would be taking responsibility for the damage and he did the usual 'We aren't liable' nonsense. I sued in small claims court and won a judgement and collected. The hotel is probably still ahead of the game by denying others' claims, but I challenged this and won. I hope more people will try it too.