One textbook for high school military cadets says girls should wear lipstick when in uniform. Another offers what a history professor described as a “frightening” interpretation of how the Vietnam War was lost. Another blames the death of Kurt Cobain, the Nirvana frontman who fatally shot himself in 1994, on heroin addiction.

A majority of public school textbooks receive extensive professional and government vetting, undergoing revision, rejection and public debate. But the Junior Reserve Officers’ Training Corps, in courses taught at thousands of high schools around the country, uses textbooks that have bypassed those standard public reviews.

The J.R.O.T.C. curriculum materials cover a wide range of subjects, with lessons on financial literacy and public speaking, on healthy eating and first aid, on preparing for college and life in the military. Most of them offer a presentation similar to what might be found in any public high school study materials.

But a New York Times review of thousands of pages of the program’s textbooks found that some of the books also included outdated gender messages, a conservative shading of political issues and accounts of historical events that falsify or downplay the failings of the U.S. government.

A textbook produced by the U.S. Air Force informs students that the United States entered the Vietnam War after the North Vietnamese attacked a U.S. destroyer in the Gulf of Tonkin in August 1964.

But the authors never mention a key part of the story: It was the report of a second, full-on attack two days later that led Congress to approve America’s escalated involvement in Vietnam — and that attack, history eventually revealed, never happened.

A review of that history published by the U.S. Naval Institute concluded that the second incident did not happen and that U.S. officials, including the nation’s defense secretary, “distorted facts and deceived the American public about events that led to full U.S. involvement in the Vietnam War.”

A textbook that the Navy distributes to J.R.O.T.C. students is more forthcoming than the Air Force book but says only that “evidence gathered later seemed to indicate the alleged attack may never have occurred.”