There is another article on Wired that says more about this:
Gilmore says he does not have a state-issued identification or driver’s license and that the identification rule, unlike searches for weapons in carry-on bags, does not make the country safer.
“I’m not willing to show my passport to travel in my own country,” Gilmore said in an interview. “I am not willing to have my rights taken away by bureaucrats who issue secret laws in the dead of night.”
The identification requirement dates back to the Clinton administration, which put the measure in place just after the explosion of TWA Flight 800 in 1996. Terrorism was initially suspected as the cause of the disaster, though it was later determined that a faulty fuel tank was to blame.
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During check-in, I don’t see a way where you can get out of showing your ID. If you have an online e-ticket, you have to show your ID and credit card to make sure that you are the person mentioned on the ticket. If you are planning on buying a ticket at the counter, you’ll have to show your ID to confirm who you claim to be.
Also, I always thought that airports determined whether you show your ID or not prior to boarding (not check-in/x-ray). For example, I have to show my ID prior to boarding in Atlanta but not in Boston.
Seems like it is carrier specific in some cases: http://www.kevincoffee.com/airlines/fly_with_id.htm (or check any airline’s site and their check-in procedures)