Factoid 401 - Harvard’s 1-1, 1874 football team: why does Harvard not claim this as a National Championship?

In 1874, the fifth season of college football, Harvard went 1-1 and was awarded the National Championship by Parke H. Davis. So why doesn’t Harvard claim this as a National Championship?

In that same year Princeton went 2-0 and was retroactively awarded a National Championship by the Billingsley Report and Parke H. Davis. Yale went 3-0 and was retroactively awarded a National Championship by the National Championship Foundation and Parke H. Davis.

In this year none of the three National Champions played each other, so why shouldn’t Harvard claim this as a National Championship? Why not? It makes no sense.