This is not correct. You will just be subject to considerably more screening.

"We understand passengers occasionally arrive at the airport without an ID, due to lost items or inadvertently leaving them at home. Not having an ID, does not necessarily mean a passenger won't be allowed to fly. If passengers are willing to provide additional information, we have other means of substantiating someone's identity, like using publicly available databases."

http://www.tsa.gov/traveler-information/acceptable-ids