I think the PP was referring to distribution. Disney makes movies and they distribute movies. For example, Pixar made movies, and Disney distributed them until Disney bought them out. Some films are both made and distributed under the Disney name (like Frozen), while others are made and distributed entirely by Touchstone (such as Gnomeo and Juliet). Since Touchstone is entirely owned by Disney, you could say that Disney indirectly made Gnomeo and Juliet.
I know some of the Touchstone films have played on the ships, but I am not sure if they all do.
Disney entered into an agreement to distribute 30 Dreamworks films, but to my knowledge, none of these have played on the ship. Either way, Rio 2 is distributed by 20th Century Fox and I don't think they have any relationship with them.