That is actually not accurate. As far as stability, Solid plank lumber such as Oak, Maple, Cherry, Mahogany and others are just fine for paneled cabinet doors (solid rails and stiles with glued and routed panels or furniture grade plywood panels). They are also fine for draw fronts. If they are kiln dried properly, they should handle the heat just fine. Moisture is actually the biggest problem and not the heat specifically. The heat certainly affects how dry the wood can become, whereas humidity affects the moisture content and warping. As far as cost, the North American average today is: Solid oak plank lumber typically costs $5.00 to $14.00+ per board foot, furniture-grade plywood runs $2.50 to $5.00 per board foot equivalent, and MDF is the most economical at $1.30 to $2.50 per board foot equivalent.
Have you ever seen a solid exterior door to a home or building made from MDF? Of course not. The extreme elements of sun, heat, cold and water would destroy MDF in shor order.
So as you can see, the comparisons are not even close. While MDF is certainly stable when not subjected to moisture, it is by all measures an inferior building material.