To a remarkable degree, the Robinsons have been able to control story-telling about ''the Forbidden Island,'' as local people refer to it. It is common for a professional man to say, when imparting some lore about Niihau, ''Don't use my name.''

The Robinsons have refused for decades to permit reporters to ride over to Niihau on the World War II landing barge that carries provisions in.

Officials from public agencies, however, visit there freely as their duties require. Dr. Mitsugi Nakashima, the district superintendent of schools, said he had visited it ''a number of times.''

He described the island as very dry, the buildings of sawed planks as ''very weathered,'' and the life as ''simple in the extreme.'' There is no electricity on Niihau, nor is there a system for piping water into the houses. Kerosene stoves are used for cooking.

Rainfall is caught on roofs and moved into barrels at each home to augment the communal water supply. 34 Students at School

The Robinsons' Niihau ranch has 63 jobs. The ranch owns all the buildings, including the three one-room structures where teachers paid by the state are instructing 34 students this year.

All three teachers were born on Niihau. The teacher in charge is Jean Keale, who holds the island's only teaching certificate. She is one of only two Niihau grade school graduates to earn a college degree. The other is Mrs. Keale's daughter, Jean Beniamina.