1992 Ford Tempo crud in radiator, dirty coolant

1992 Ford Tempo mileage: 65,000. My daughter has a 1992 Ford Tempo that she has been driving for about 4 years. She is very conscientious in regularly changing oil, and routinely having it inspected by a mechanic. She bought the car used, with about 50,000 miles on it. Recently, she has had a situation where her antifreeze becomes brown - at times like mud. She has regularly, especially before winter, had the system completely flushed and new antifreeze added. However, at regular intervals, usually every oil change around 3,000 miles, it is again filthy brown. Our mechanic states that it is rust and corrosion from the inside of the radiator, but when I asked him if he advised replacing the radiator, he said he did not feel that would help or solve the problem. He feels the motor - block, valves, etc. Are sources for "crud" that ultimately makes its way through the cooling system and creates the filth in the radiator. He suggested that the only way to completely eliminate the problem was to tear down the motor and clean up the source of the dirt and matter. This is not advisable based on the age of the car and the costs associated with doing this type of major cleaning. He also said that he has seen cars with similar dirty radiator coolants run and last for years - provided of course the radiator is periodically checked and back flushed with new antifreeze added. Any opinion on this recurring problem and the advise of my mechanic. My daughters many miles away at school and I am naturally concerned especially when she has a 3 hour plus drive home alone when she visits during the holidays and breaks.