No, this is not correct. There is very much a tradeoff, definitionally. “Allocative efficiency” refers to producing goods and services that meet consumer demand, e.g. producing the colors of cars that people want to buy. It is future-oriented, generally. However, Pareto efficiency (rather, optimality) is where a person cannot be made better off without making someone else worse off. The two concepts are related (sometimes) but not the same thing at all. To expand that thought a bit, Pareto efficiency is about finding the correct balance between allocative and productive efficiency, not just concentrating on allocative efficiency alone1.
The person who wrote that is confused and should read their textbooks again, but more closely this time.