How is the resolution of the conflict dependent on Mr. Martin's personality in James Thurber's "The Catbird Seat"?

Erwin Martin is a creature of habit, set in his routines
and habits. The plot that he hatches to unseat his nemesis, Mrs. Ulgine Barrows, is
dependent upon him breaking every code of his personality. He doesn't curse, he doesn't
drink, and he doesn't smoke. His milquetoast demeanor seems to be ironclad, and Martin
appears totally incapable of change. His boss, Mr. Fitweiler, knows this, so when Mrs.
Barrows comes to him with the astonishing tale of Martin's visit to her apartment, it
seems like an impossibility. He can either believe Mrs. Barrows' incredible story, or he
can trust his instincts about the meek and unchanging Martin. Fitweiler, of course,
cannot believe Mrs. Barrows--exactly as Martin had expected--and Martin's job remains
safe.