This is an older, but more recently posted YouTube interview where Sherwood Schwartz is asked about what music John Williams did, at 3:28. Not sure if it reveals anything people here don't already know. But Sherwood is clear that Williams wrote what he calls Gilligan's theme (and he less assuredly credits him with Skipper's theme). He also avoids crediting Williams with the opening theme music. Wikipedia for Gilligan's Island credits Williams with writing the calypso music for the opening theme of the unused pilot. The Wikipedia page is seemingly responsible for spreading that around to various other articles on the internet. But the sentiment on film music forums seems to be that Williams did not write that calypso music. This interview with Sherwood seems to support that conclusion. But whether Sherwood was thinking only about the official opening theme and not the unused one when he said that is uncertain.
