A baby was in fact born at Palmyra Island shortly after World War II, when his father was doing ionosperic work there for the Central Radio Propagation Laboratory of the National Bureau of Standards. At that time Palmyra Island was legally an ordinary part of the U.S. Territory of Hawaii. That baby, Leo Watts Honea, Jr. is now an engineer living in a mainland U.S. state.
Other Territory of Hawaii citizens, in the Hawaiian Islands, automatically became State of Hawaii citizens in 1959 when those islands became the State of Hawaii. Congress deliberately excluded Palmyra Island from the new State, by statute, so it is technically the the only remaining part of the old U.S. Territory of Hawaii. That's why Palmyra Island is the only remaining "incorporated" U.S. Territory (under the doctrine of the Supreme Court's "Insular Cases" decided after the Spanish-American War), because the Territory of Hawaii had been officially incorporated.
Mr. Honea may or may not be, very technically, a citizen of the U.S. Territory of Palmyra Island since 1959. This case is not clear.