This is a true statement.
Soils are said to be nutrient rich when they contain compounds necessary for plant growth. These compounds are introduced into the soil either artificially (through the application of fertilizer by humans) or naturally (through the decomposition of organic material).
There is a large amount of organic matter available in rain forests for decomposition. Things like falling plant material (leaves and fruits), animal droppings, and the bodies of deceased animals are sources of organic matter that are broken down by bacteria and insects.
Soils which are not nutrient rich are found in areas which do not have a large amount of organic material available, such as deserts. Alternatively, poor soils may also be present in areas with significant erosion which prevents the accumulation of nutrients.