While I'm certain that an MIT student could/would have come up with the slingshot idea, in all fairness, there weren't really many different ways to get the spacecraft back to Earth. Either turn around, which uses a lot of fuel, but possibly get back sooner, or use the moon's gravity to turn around, which uses less, but might take longer. Third option would be to speed up, still use the moon, and achieve the same effect. I'm pretty sure at the point that they were deciding what to do, NASA had pretty much every employee awake and on the job. It's a bit presumptuous to assume that none of them came up with the slingshot idea on their own, considering going into an orbit of the moon was part of the initial plan of the mission in the first place.
What I CAN see happening though, is considering the time crunch the engineers were under to figure out what to do and implement that plan before the astronauts died, is that the student submitted the idea immediately, it got added to the list of ideas, and he was given attribution as a result of being the first one to voice it (even though hundreds of others probably had the same idea). The student wasn't really responsible for saving the mission, he just got first post.