White's volumes are far better documented than Draper's and far more damaging, because the footnotes gave the argument an authority that outlasted the checking of them. Several of the stories he put into general circulation are now known to be false, and the most famous concerns the shape of the earth.
The claim is that medieval Christians believed the earth to be flat on scriptural grounds, and that Columbus had to overcome churchmen who told him he would sail off the edge. Educated Europeans had known the earth was a sphere continuously since antiquity; the dispute with Columbus was about its circumference, which his opponents estimated correctly and he did not. The flat earth story appears to have entered popular history through Washington Irving's romantic life of Columbus of 1828, and it was White's account, with its apparatus of references, that fixed it as established fact for the following century of textbooks.
Other set pieces have gone the same way, including the picture of a church that forbade human dissection and the picture of universal ecclesiastical resistance to anaesthesia in childbirth. The pattern is consistent: a real incident, a real objector, and then a generalisation from one hostile cleric to an institution and an age. The atlas records the warfare literature as a historically important position with identifiable authors and identifiable errors, which is what it is, rather than as a description of the past.