Why would engine fire cause loss of control?
In general, an engine fire in a modern jet airliner should not cause a loss of control. 

Even though engine fires are rare, pilots are highly trained in dealing with them. Once detected, pilots are able to cutoff the supply of fuel and hydraulic fluid to the engine, and then discharge fire extinguishing agents. Even if the fire was not extinguishable, it would most likely not damage the wing structure or controls since the heat and flames would be directly away from critical systems by the forward movement of the aircraft.    

An "uncontained" catastrophic engine failure where parts of the engine penetrate the aircraft wing and fuselage could possibly cause major damage to critical systems. There have been some incidents of uncontained failures that resulted in a loss of control and fatalities. 

Here is a list of Notable uncontained engine failure accidents

Three of these accidents resulted in a loss of control and fatalities. The most notable was United Airlines Flight 232 where the failure of the rear General Electric CF6-6 engine caused the loss of all hydraulics forcing the pilots to attempt a landing using differential thrust and resulted in 111 fatalities.