No, it is not a mistake but the reverse colors on the battle flag were somewhat a rare variant. Two examples survive that I know of and of course there may be more. General Richard Taylor's western command used a reverse color square battle flag but without the white edging around the cross as was more common of the "semi official" battle flags of the Confederate armies. Also there exists the garrison flag of Fort Fisher (south of Wilmington, NC) which was captured upon its surrender on January 15, 1865. This flag was a second national Confederate States pattern which utilizes the battle flag as it's canton. However, in this case the colors of the canton were reverse with the field of the canton being blue and the cross being red, edged with white trim. Another flag comes to mind that General Leonidas Polk's corps used early in the war. It was a battle flag with a red upright cross, (known as St. George's cross) instead of a saltire (known as St. Andrews) on a blue field.

Regards,
Michael