Actually, you can board a plane with no ID whatsoever. It's not easy, and would most definitely take some time, but it happens all the time. Having Alex with his credit card and ID to vouch for him would help somewhat. I travel a lot, and have asked the TSA agents about this, as I couldn't find my ID for about five minutes one trip. I've got a backup, but it still panicked me.
Remember that Alex paid for the tickets and pretty much everything else in Detroit.
The great Mike Rowe posted just a couple of weeks ago on getting to the airport with no wallet or ID. Fortunately for him, he had two magazines with him on the cover in his carry-on bag.