Lets see. Plane lands and needs de-iced. That is done before passengers board. Pilot looks out the window and sees the wings beginning to frost up. Best plan at that point is to put the passengers on, and then when they are on, de-ice the aeroplane again. probably just the tops of the wings..? That gives you the shortest time from de-ice to take off. thus minimising the possibility of further icing problems.
Yes you could have been in duty free, but the clock starts ticking the second you start the de-ice process. It is called holdover time. The scenario could unfold... de-ice. Half an hour to board, close doors, wait for start... more ice. Now we need re-re de-iced. All off so you can go back to duty free, de ice, re-board, more ice, all off again, de ice, miss slot..de- ice, board.. wait for yet another slot, more ice, all off to duty free, de-ice, all on after another half an hour, more ice, all off, back to duty free...
But you clearly know better.