Why Does Only the Navy Operate Military Reactors?

When I posted my Submarine Humor entry, I included my favorite piece, obviously written by what appears to be a team of bitching nukes comparing working at McDonald's to being a submariner. One of the entries may have confused some people, so I thought I'd give you the background. Here's the entry:
52) McDonald's never had an accident that cause a person to be stuck to the ceiling impaled on a french fry. (ie. No Mc-SL1)

The SL-1 was a prototype reactor set up in the Idaho desert that was built as a demostration model for a proposed series of low-power reactors to provide electricity to remote Army posts. (This excellent article has the full story.) On January 3, 1961, at about 9 pm, the reactor somehow went "supercritical" and suffered a steam explosion, killing the entire three man work crew; from the article:

Two of them died instantly, one thrown sideways against a shielding block and the other straight upwards, where one of the shield plugs pinned his body to the ceiling...

The article later discusses how the body of the man pinned to the ceiling was recovered:

The third man finally was found. His position directly above the reactor presented a new hazard. Aside from the obvious difficulty of working in a high radiation field at an awkward location, physicists feared that if pieces of debris near him fell onto or into the reactor through the open shield-plug holes, the disturbance might start a chain reaction. A photographer suited up and entered the room for one minute, taking as many photographs as possible. With the help of the photos, a plan took shape for the retrieval. Army volunteers from a special Chemical Radiological Unit at Dugway Proving Ground wanted the practical experience offered by the challenge of removing the body. The twenty-four enlisted men and five officers perfected a plan and rehearsed their moves on a full-scale mock-up of the SL-1 erected at Central. They rigged a special net on the boom of a crane and positioned it to prevent the body or anything else falling onto the reactor. Metal workers shielded the crane operator’s cab. On January 9, eight men, paired in two-man relays limited to sixty-five seconds inside the building, recovered the body and lowered it to the ground.

And that is why the Army doesn't have a nuclear reactor program. As far as why the Air Force doesn't, I can't find it on an unclassified site, so I guess I don't know why...

Rumor control: Around Idaho Falls, there's always been a rumor about the "true cause" of the SL1 prompt criticality. I won't write it out, but it's buried in this comment thread...