I disagree with this statement because sometimes cheap restaurants use low grade ingredients that make their meals very unhealthy. The quality is paid!
I think it depends because I know some cheap restaurants which cook fast food and unhealthy, and other cheap restaurants which cook with few oil, boiled or baked and their dishes are healthy.
I don't think it's true because you can eat a lot of food with a lot of fats in cheap restaurants but the quality is usually bad