Cook claimed to have achieved the first summit of Denali (also known as Mt. McKinley) in September 1906, reaching the top with one other member of his expedition. Other members of the team (e. g., Belmore Browne), whom he had left lower on the mountain, immediately expressed private doubts. Cook's claims were not publicly challenged until the 1909 dispute with Peary over who had first reached the North Pole. Peary's supporters then publicly alleged that Cook's claim of ascent of Denali was fraudulent.

In 1910 Cook is proven to have lied about his ascent when another group, the Mazama Club, attempted to follow his alleged path to the top and detected that it deviated more than 10 miles from the actual way to the peak.