I'm not a lawyer personally, but I was raised in a family of lawyers and other law practices. In terms of actually winning such a case (if it were even brought to court), I seriously doubt the opposition has a case at all. But as someone who also knows how the media and big corporations work, the chances of winning likely isn't what would concern Disney anyways. It wouldn't surprise me if these people filing lawsuits actually think they have a chance of winning (likely no chance), but Disney likely doesn't have any concerns about winning either way.
The problem is that Disney may actually be concerned about the negative spin the mainstream media would inevitably give them if they chose to pursue the case in court. Even with a 100% chance of winning (probably not a far off estimate assuming the court does its job properly), Disney may actually prefer to concede to these idiots' demands rather than pursue the case in court and draw the media's eye. It's one reason they turn a blind eye to what crap guests pull (theft, vandalism etc) without repercussion. It remains to be seen how far this farce is allowed to be taken.