It's important to recognize the distinction in sport between a Championship and a Title.
A Championship is won on the field of play against direct competition. A Title is awarded by an organization to a team for perceived merit. Winning a Championship always includes a Title. Being granted a title is an honorary achievement and doesn't infer a championship.
I'm glad we only count our Championships!
If other schools want to count their "titles" then they should say "National Titles" and not "National Championships". If we want to count our Helms, I'd only include the 1933 title before the NCAA Championship was established in 1939. We have "9 National Titles", and we have "8 National Championships".
The situation in football, of course, is MUCH worse. There were no championships before the BCS/CFP era. So it's a nightmare trying to keep up with the "Titles" granted by various foundations and polls claimed by Notre Dame, Alabama, Michigan, etc.