No. That's not 100% true.
You can use any app that doesn't require Wi-Fi to run (such as Flashlight, Dactyl, iChoose...etc.)
Apps like Google Earth, Air Sharing, AIM, or Urbanspoon do require Wi-Fi to be used.
Basically, there are apps that do need Wi-Fi to run, and there are those that don't.
Edit: big-blue-wolf beat me to it. Basically what he said. 😛