In the two Helms title seasons, KU played a combined 4 games outside of the Missouri Valley conference (3-1 record) that stretched through Missouri, Iowa, Nebraska, Kansas and Oklahoma. The league included Drake, Grinnell, and Wash U (St. Louis). KU did extremely well, but calling it a "National Title" is absurd. It was a regional, or better yet, a league title*.
*shared with Mizzou in the 1921-'22 season.