JennX is - so far as I've seen and talked to people about - correct.* TSA is under orders (it's the main reason they are there) to make sure the person getting on the plane is the person on the ticket and that they have legal photo ID as such. (Why, I ain't got a clue, all the 9-11 highjackers had ID, so it would not have stopped them). That, and making you walk through the medal detector/radiation scanner/pat-down. And because there are in the end only two things for the TSA to do (despite the huge apparatus that's there to enforce it - call it 'security theater'), and they are the law, and they are being HEAVILY supervised, they tend not to let either slide.
So...just like there is NO way to get on a plane w/o doing one version of the second, it's going to be equally hard if you are standing there with an ID that does not look like you. No matter how understanding Mister TSA Man is, they pretty much CAN'T let anyone through who doesn't match their ID. All they/you can do is get the supervisor involved because they don't' have - nor should they - have much leeway in their decisions, and my experience is that once they call in their supervisors then you're really hosed, as they truly ARE jerks. (Also, from that point on, you really can't just get up and walk out - you're not under arrest, technically, but as soon as they pull you over/out of line you could be, call it double secret probation.)
So tell your friend, that from what I've seen, the indignity of having to get a new ID is a lot less than running afoul of the TSA (who seems to have a whole lot of people with little to do EXCEPT harass people), and given the general indignity (because cattle are treated better on their way to the feedlot) of flying in the first place these days, that having to get a new ID is just one more abuse, and perhaps not even the worse abuse, in the Modern Aviation AbuseStack.
Update the photo.
*I'm a seasoned veteran of air travel, including a few pre-jet age flights under my belt, DC-6. My dad flew for an airline and I grew up at airports and I KNOW airlines all too well, so someone who get's to the airport long, long in advance of the flight (just in case my flight is canceled I like to get there with enough time to make them change me) and hence has spent a lot of wasted hours watching the whole TSA song and dance. Airports are fantastic for people watching - you got winners, losers, celebrities and everyone else, its' a trip - and watching them interact with TSA Security Theater is one of the best places to watch people. Even real famous people - people we all know from TV and stuff - have to do TSA. Equality for all. So if you are concourse side (not on the terminal side) then you are watching all these people come toward you and get to watch how they react to playing stupid human tricks in an airport. The whole 'shoe thing' just quadrupled the fun, because that's just kind of weird and demeaning at the same time. Let me tell you there are equal parts hilarity and sexy in watching the TSA Shoe Dance.