No, the reactor was built *in* Mathews House, under the bed of one of the builders (Justin, because he lost the coin toss). I lived right on the other side of that wall for a year.
Furthermore, the reactor was *not* dismantled at the orders of the judges. Fred found it in the back of his truck, still running, a few months later. I don't know what happened to it after that.
The physics majors in question did not use the nuclear material to which they had access, because, as Fred said, it would be pretty silly to use plutonium (the Physics Dept's neutron howitzer) to make plutonium. Their original material was thorium, from the inside of some old vacuum tubes (although their first plan involved americium from ordinary hardware-store smoke detectors).
The one thing they had to borrow from the Dept was the equipment needed to prove plutonium production. *THAT* took a lot of begging, and was the hardest part of the whole thing.
The list item was inspired by a Reader's Digest article about the "Nuclear Boy Scout", who built a breeder reactor in a shed in hopes of making Eagle Scout (he made a Superfund site instead), so, really, any whacko with enough nerve and enough physics books could probably do the same.