The era of national champions being decided by polls didn't begin until 1936, when the AP poll started. In 1926, the only national championship award in college football was the Rissman Trophy. It was awarded based on the rankings under the Dickinson System. Frank Dickinson was a professor who devised a mathematical ranking system based on strength of schedule. Sort of the Sagarin of his time, I guess. Dickinson's rankings were the first widely publicized and widely accepted rankings, and the Rissman Trophy was the first national championship award (and in 1926, the only award). Stanford was declared the national champion under the Dickinson System and won the Rissman Trophy in 1926.
A number of ranking systems were developed later. The sponsors of some of those ranking systems have gone back and retroactively declared national champions for seasons previous to the creation of those systems (including Boand, Houlgate, Poling, Helms, Parke Davis, National Championship Foundation, CFRA, and others). Those retroactive rankings are the basis for the national championship claims of other schools for the 1926 season. But at the time, Stanford won the only recognized national championship award and was viewed as the national champion. In my unbiased view, that gives Stanford the best claim to the 1926 championship.
A number of ranking systems were developed later. The sponsors of some of those ranking systems have gone back and retroactively declared national champions for seasons previous to the creation of those systems (including Boand, Houlgate, Poling, Helms, Parke Davis, National Championship Foundation, CFRA, and others). Those retroactive rankings are the basis for the national championship claims of other schools for the 1926 season. But at the time, Stanford won the only recognized national championship award and was viewed as the national champion. In my unbiased view, that gives Stanford the best claim to the 1926 championship.