Based on the fact the group kept a diary that they updated every day, and also that their last campsite in the valley is known and the date they camped there is recorded in the diary.
But I agree that the authorities shouldn't have been so sure... they knew the group didn't break camp and move on from the slope, so it can be assumed they died within a day of setting up the tent there... but I think it should have been considered a possibility that they (or some of them) remained there for multiple days for whatever reason, or even that they didn't all die on the same day, for example those who managed to build a snow cave (if that's true), had some chance of surviving for a few days, they had drinking water as the stream was nearby. They had firewood and matches.