Although this would be true, especially on cold winter's nights, the fires are also lit during the daytime and when the nights are warm. There is better answer. They only agreed because of their traditional politeness. It is likely that the parents agreed because of their traditional eagerness to avoid confrontations. However, it is not likely that they saw no connection at all between the child's ill-health and the smoke.
Smoke makes anybody's eyes water and too much of it makes anybody cough.
There was another reason why they did not shift the fire.