In the old days of copper and brass radiators this was true. More rows meant more surface area in contact with the fin and consequently a higher heat rejection. So a 3 row was better than a two row and so on.
When aluminum radiators came around the rules changed. Cooling engineers concluded that by lowering the fin height you could stack more layers of tubes. In addition, using wider tubes would increase the tube-to-fin contact area. The end result was a very high performance radiator with a huge savings in weight.
The U.S. standard for performance aluminum radiator tubes is a 1.0" wide tube and imported radiators have smaller 16mm (.62") tubes. In this case a 3-Row aluminum radiator would only have a total of 1.86" of tube-to-fin contact surface which is less than the two row core with 1" tubes. The online ads for these 3-Row aluminum radiators will indicate several features of the radiator design but they avoid the issue of the tube width. DeWitts radiator goes another step and offers a two row core with 1.25" tubes or (2.5") tube-to-fin contact and this would again exceed the performance of a 4-row imported core design. So, if you are researching your next purchase ask about the tube width. That will tell you a lot about the heat rejection and the origin of the product.