We have been to WDW several times since 2000. On every one of those trips at least one member of our family has been picked to be in a show or for something special. DH was picked to be in the Shamu show at Sea World (I'm still SO jealous of him for this...I wanted to pet Shamu!!!)
Last year we were all picked to be the "Magical Moment Family of the Day" at the Lights, Motors, Action Stunt Show. Every time we have been picked out of the crowd (we were approached by a CM at the fastpass machine for the stunt show). The CM's have always told us that they rarely pick people who ask. They say they try to judge by how happy a family looks and if they really seem to be enjoying themselves. That seems to be a good policy and I like the fact that some things are still random. That makes it all the more special when it happens.