Things I learned in this thread...
1. Football doesn't count before 1970 (which given Nebraska's performance is an understandable bit of cherry picking).
2. The 1970 & 1997 championships don't count because of 'everybody gets a trophy' ties.
Ohio State claims 8 national championships.
Six of those are undisputed.
1961 & 1970 are the questionable ones. Each of those was selected by a single recognized 'major selector'. Those being the Football Writers Association of America & National Football Foundation respectively.
1942 - AP Champs - The coaches poll wasn't introduced until 1950
1954 - AP Champs - UCLA was #1 in the coaches poll but prohibited from playing in the Rose Bowl due to the no repeat rule. USC was the conference rep, losing to Ohio State.
1957 - UPI (coaches poll) Champs - The AP selected Auburn who was barred from participating in a bowl game due to being on probation (imagine that).
1968 - Voted #1 by all of the major selectors...AP, UPI, FWAA & NFF.
The answer to the initial question posed is "when you are once again the one being used as the benchmark in comparisons".