Correct... Disney is not the exclusive rights holder to Peter Pan. It was written by James Barrie and after he died he left the rights to a London children's hospital (Great Ormond Street Hospital for Children*) while still owns the rights today. Disney is only a license holder for the use of Peter Pan, but it's not an exclusive license like they hold for Winnie The Pooh (owned by a London dinning club after being willed it by A. A. Milne). It's like Tarzan, Disney made the film after licensing the charaters and basic story line from the estate of Edgar Rice Buroughs.... but theirs isn't the only Tarzan flick on the block.
Ironically, up until recently Disney was going to do the merchandise marketing for the new Universal Peter Pan film, but backed out after a licensing dispute with the hospital's lawyers. Disney holds a license to sell Peter Pan merchandise. Apparently the hospital interpretated the license only applied to merchandise related to the Disney films, but Disney read the text as applying to "Peter Pan" (Dinsey or not). Disney felt they were being asked to pay for the rights twice and baked out of the deal. Some of the UK media branded Disney as wanting to steal money from sick children.
* = In "Hook" (another non-Disney Peter Pan film), "Grandma Wendy" is honored for her work and donations to the real hospital by name.