As Gilligan is falling off the cliff while walking backward, he is wearing the Skipper's hat. When Gilligan is shown hanging from a branch, he is wearing his own regular hat.
In the opening sequence, when the Professor & Skipper are talking to Gilligan about the ceremonial headdress that was found, it is the PROFESSOR that identifies it as Papuan & gives details about it. Later in the story, after Skipper returns & says that his kidnapping was a test for Gilligan, HE admits to planting the headdress to give the impression that there were natives on the island & shows a label in the hat that says, "Made In Paris." Mrs. Howell states that the hat is hers & that she must have left it on the island somewhere. It is not feasible that the Professor would not have known the nature of the hat, since it was not authentic & he would have found the label during thorough investigation AND he is somewhat of an expert on Polynesian cultures as well as knowing some languages.
When Gilligan goes over the cliff after marching backwards, he is wearing the Skippers hat. When he is seen holding onto the branch protruding from the cliff, he is in his own hat. A similar scene takes place in #2.8;"Agonized Labor. The scene in #2.11 is most likely extra previously recorded footage.