Interesting dissertation idea!
A good place to start looking for "rumors" (particularly primary sources) would be GoogleScholar. I'd recommend a JSTOR, Academic Search Complete, and a handful of other lovely online journal databases, but I've searched a majority of them already for info on Peter Pan but I don't recall finding anything regarding public response to the play/movie adaptations.
Checking just now on EBSCO, I've found an article titled "A Hundred Years of Peter Pan" written by Peter Hollindale (Children's Literature in Education, Sep2005, Vol. 36 Issue 3, p197-215). It may be worth a look...
Regarding more modern takes on the story (ie. Disney's Peter Pan, Spielburg's Hook, and Hogan's Peter Pan (2003 live action)), you'll no doubt be able to find some critical reviews of their release. If I recall correctly (it's been more than ten years since I've seen it), Disney released some background information on the production of Barrie's original as well as the animation and production of their movie at the end of the presentation. You may be able to access this on YouTube, and, if not, it's no doubt still on the DVD (or VHS, if you prefer).
It would be interesting to note in your dissertation how the presentations of Peter Pan have changed from year to year, commenting, for example, on the evolution of political correctness. One of the more recent productions of Peter Pan (by the Royal Theatre of Scotland, I believe), omitted the Indians from their production because of the now racist lines and remarks found in Barrie's original script.
Best of luck on your research and writing!