How could using an ungrounded appliance with a grounded extension cord be a fire hazard?
The Fire Dept is wrong - it is perfectly normal to plug a device with a 2-pin plug into a 3-hole socket.
Breaking the ground pin off a 3-pin plug, then plugging that into a 2-hole or 3-hole socket may produce an electrical hazard - possibility of a shock.
If a high-current load, like an electric heater, was plugged into that burned outlet, and the contacts made poor contact, that would cause the overheating and resulting fire, whether the heater had a 2 or 3 pin plug.
The statement by "Barrie" is nonsense, many devices don't have a ground connection and thus only have a 2-pin mains plug. Such devices are "double insulated" and have the 2-squares logo and possibly some text like:
The damage of that power strip was very likely caused by a short circuit and/or overload. There is no ground/earth connection required for that to happen. Likewise it is unlikely that a ground/earth connection would have prevented that damage from happening.
Connection a 2-prong device into a 3-prong socket is OK. Properly designed 2-prong devices are isolated and don't need protective earth.
What is dangerous is plugging a 3-prong device into a 2-prong socket, or using a 2-prong extension cable with a 3-prong device. That will cut the protective earth wire on an appliance which needs it, exposing the user to electric shock upon failure inside the appliance.