The title of the film derives from what was expressed by the Swiss during World War II, for as a nonbelligerent country many refugees desired entry there, with most being denied permission. They were frequently told, "Our boat is full," a reference to passengers of a lifeboat after a ship sinking frequently refusing to allow any further survivors to enter their craft after it had reached a level of occupancy felt to approach the limit of safety.
Plot
In 1942, six individuals manage to escape to neutral Switzerland during the Second World War. However, in August of that year, Switzerland decides to tighten its admission criteria. The six attempt to meet these criteria by exchanging clothes, roles, and papers, with some cooperation from villagers. Yet, the village policeman sees through their deception, feeling betrayed, and initiates the official procedure. As a result, those persecuted due to racial motives are forced to leave, while those politically persecuted are permitted to stay.