Actually, it is indeed true that they could open themselves up to liability, there are various sites that have the information about it. But, the letter of the law does seem to read that any private company that requires a vaccine that only has emergency authorization can be held legally liable for the damages a person suffers from the vaccine. There is absolutely no doubt that this applies to employees, basically if a company requires you to get the COVID vaccine (or any treatment that only has emergency authorization and not full approval) to continue working there, they are liable for all damages. The slightly gray area is does this also apply if a company requires a customer to get the vaccine in order to continue being a customer, are they liable? This is why I said they could be opening themselves up to liability and didn't say the definitely would. It isn't something that a court case has been decided on with it yet, but there are some currently in the works.
This isn't something that has been explicitly written, as no one would ever have thought that companies would try to require their customers to show proof of vaccines, especially ones with emergency authorization. So, it will be interesting to see what side the courts come in on this in the end, but the point is valid that they could be in for a world of hurt if they try and I just don't see Disney opening themselves up to that mess.