The linked story is a great example of why you should never listen to what old men remember about great events and their (often "heroic") part in them. At no time did NASA need some graduate student from MIT to help them with a Guidance 101 type problem on Apollo 13. The difficulty was in getting the Lunar Module prepped quickly enough to make a small burn that would get them on a free return trajectory, the same type used on the previous four Apollo missions to the moon. Apollo 13 was the first to use a less safe trajectory so they could visit a more interesting place, Fra Mauro. There were always many ways out of a pickle and abort guidelines had been carefully developed for different phases of the mission. At the point of Apollo 13's explosion, a direct abort going straight back was never possible, not least because their big engine was in the now dead Service Module. Free return was the only option.
There *was* a very famous "hippy" type guy at the MIT Instrumentation Lab, Don Eyles, who was responsible for much of the Lunar Module's landing program. On Apollo 14 he was instrumental in solving a problem that would have prevented that landing and he did get official recognition for it and there are pictures of him with his long hair and mustache. So that's another part of the Gizmodo crap article that is wrong.
As far as the photos of the Apollo 11 astronauts on the moon go, there were about three pictures taken by Aldrin with Armstrong only incidentally in the frame. The shot with the flag is definitely of Aldrin, as you can see Armstrong taking the picture in the 16mm film taken from the Lunar Module window. Aldrin, unconsciously or deliberately, never took a proper picture of his fellow crew member and commander. It was only after Apollo 12 that a photo specialist at the Houston space center suggested red armbands for the commander to distinguish him in the photos and Jim Lovell, the Apollo 13 commander, never got to show them off, alas.