Correct - at the time the 320 family was being designed the 737-300/400 was the longest range 737 available (not counting the BBJ version). So Airbus designed the 319 to have more than transcon max range, the 320 to have nearly transcon range (max range was transcon but alternate fuel requirements shortened the effective range) and the 321 even at max range wasn't able to do transcons. Airbus added a center section with more fuel capacity to the 321 and achieve mostly transcon range with normal headwinds westbound. If memory serves, and more and more it doesn't, US was the N. America launch customer for the longer range A321.
Jim