The rights referred to are those associated with the intellectual property that Disney owns, including the image of its recognizable characters and buildings. The rights to exclusive use of and protection of intellectual property is granted by the law, not by us guests "swearing" anything.
Actually you have to swear(at least what I heard) when you do a backstage tours and you are not allowed to take pictures at every area, but you can take picture/videos of everything else on a regular admition, and you can place those on any fan site/ facebook and so on and every of those sites run some sort of ad on every page, does not mean they get popular because of Disney pictures.
Disney has and will sue, in case of infractions, especially if they're forced to in the manner referred to earlier. Generally when they sue, for things like this, they sue for the legal remedy known as "specific performance" (i.e., in this case, that the offending video be taken down), not for damages. And in the case of
YouTube, they won't even go to the person who posted the video, but rather directly to Google. In that situation, it is Google that is committing the transgression that Disney cares about.