Unnecessarily reductive. It's both the ceilings and walls. There is no single solution. We also have no idea of they have an attic or vaulted ceilings. An attic full of hot air is a heat bank that will radiate into the living space all night. All insulation will do is slow the transfer. Really good attic floor insulation will help retain heat in the attic, so you still want to improve attic ventilation. But, if you reduce the amount of heat going into the attic in the first place, you reduce how much insulation and ventilation you need to reach a certain cost/benefit ratio. It's usually more feasible to do half a job addressing each than it is to make just one variable perfect. So, when it comes to replacing a roof covering that needs replacing anyway, doesn't it make sense to do that as best as feasible?

Tour a home with an infrared thermometer camera in summer. I promise you, the ceiling is warm, too. You just don't hang out 3 meters up.