The difference is that Auburn was not penalized for infractions during the 1993 season. Nor were any of our wins vacated. USC was penalized for violations during the 2004 season and did have wins vacated from that season. So I think there is a clear distinction. (Also, if you are going to hold probation for previous acts against the 1993 team, don't you also have to hold it against the 1957 team?)
Moreover, cherry picking which NCs to "claim" is exactly why am against the idea that it is on us to claim anything. We are just reporting the facts, ma'am.
It is a fact that Billingsley named Auburn the 1913 National Champion. It is a fact that Billingsley, the New York Times, Sagarin, FACTS, and Football Research named Auburn the 1983 National Champion. It is a fact that the National Championship Foundation named Auburn the 1993 National Champion. No opinions. No claims. Just facts.
Of course, we also have 1957 and 2010.
2004...ok, we have to go rouge with this one. Our best argument is that USC was cheating at the time and was stripped of the championship, so it naturally falls to us. It is a dubious argument, but it is either that or don't count it.
That is my 2 cents worth, anyway.