Always happy to answer a question about Thurber, one of my favorite authors.

Jack "Pal" Smurch, the protagonist of "The Greatest Man in the World," is an assistant mechanic who has recently achieved the remarkable feat of flying a single-engine plane around the world.  He is soon going to be lifted to "the heights of fame"; the problem, however, is that he does not possess "the intelligence, background, and character successfully to endure the mounting orgies of glory" that will be offered to him.

When reporters try to dig up the story of Smurch's life, they find that it is not fit to print.  He is a "little vulgarian" who leers rather than smiles.  He is a "nuisance and a menace," who once knifed the principal of his high school and once spent time in a reformatory for stealing an altar-cloth from a church.

When Smurch is first interviewed by the press after his landing, he does not display the modesty that was expected of heroes; instead, he tells the reporters, "I put it over on Lindbergh," a disparaging reference to Charles Lindbergh,  who "only" managed to fly his little plan across the Atlantic Ocean.

Thurber seems to be satirizing the way people who performed great feats were typically portrayed in the media as moral paragons, whether they were or not.  Thurber wrote first published this story in 1931. I doubt that someone could write such a story in our contemporary times, when people like Paris Hilton can become celebrities on the basis of little else beside the irresponsibility and immorality of their behavior.