There are two stories that purport to explain the curiously out-of-place palm trees on the beach. First story: the palms are courtesy of a movie company that filmed a feature there in the 1920's. Story #2 comes to us from Jeffrey LaBarre, who wrote "I was having dinner as a reciprocal guest at the Santa Barbara YC and talking with a couple at the table next to me about my visit to Cuyler Harbor. I was telling story #1 when another older gentleman piped up. He said that, while this story has been repeated many times, it was false. The four palms were planted, he said, by a fellow SBYC member. He said he knew this was true because he knew the man and his son who did the planting and that it was much later than 1935, in the early 50's he thought (this is, I think, consistent with the size of the palms). I can't say for certain that this guy was right but it is certainly commonly accepted knowledge at SBYC and I have since heard this from other sources as well."
Frankly, we like the movie-maker story legend better, even if it's not true.