In the old days of copper and brass radiators, this is true. More rows mean more surface areas are in contact with the fins and therefore have a higher heat rejection. So 3 rows are better than two rows, and so on.
When the aluminum radiator appeared, the rules changed. The cooling engineer concluded that by lowering the fin height, you can stack more layers. In addition, the use of a wider tube will increase the contact area of the tube with the fins. The end result is a very high performance heat sink that greatly reduces weight.
The US performance aluminum radiator tube standard is a 1.0 inch wide tube and the imported radiator has a 16 mm (0.62 inch) tube. In this case, the 3-row aluminum heat sink has only a 1.86" tube-to-fin contact surface that is smaller than the two-row core with a 1" tube. Online advertising of these 3-row aluminum radiators will point out several features of the heat sink design, but they avoid the tube width problem. Our radiator is another step in providing a double-row core with 1.25" tube or (2.5") tube-to-wing contact, which will again exceed the performance of the 4-row imported core design. So if you are researching your next purchase, please ask about the tube width. This will tell you a lot about the source of heat and products.