This issue has to be blamed first on the family which forgot the passport first, second the airlines that issued a boarding pass for the family at Boston, and finally the Indian immigration officials.
First, Though any human can make mistake, no one will make this sort of mistake when they are travelling long distances, coming to india on long vacation after long time.
Second airlines issuing boarding pass should check whether the passengers are going with valid documents. Similar happened for me when i boarded flight from new york to dubai. but the airlines told i cant go as i didnt have a valid visa. As emirates gives a on arrival visa at dubai airport i was allowed to board the flight, for which i have to pay to emirates.
Finally, indian immigration officials should be blamed. these officials should have atleast given the time the family had requested, which would have been a nice on the part of the immigration officials. if the fax was not received then the family should have been sent on the next air france flight the next day and made the family to stay in the airport till they board the flight.
