A few things come to my mind reading those 2 links....things that I'm sure have crossed my mind about this whole issue in the past, and things I'm sure have crossed the minds of many, many other Gamecock fans:
First off, an argument has been in the past that the NCAA technically have not awarded or named any college FB programs with titles of national championships. That has always been done by the media and consensus of general population (national polls). Therefore, when a NC program is found to have violated NCAA rules during it's NC run, the NCAA can penalize the program with sanctions: reducing scholarships, having games involving ineligible players voided from record, banning post-season bowl eligibility. But they typically have left it up to others if the national title should be stripped.
Of course the NCAA went beyond that regarding SoCal in 2004, but I believe one of the games deemed voided was SoCal's bowl win that earned them the national title, and then the AP or someone decided that since the NCAA voided the game they played that won them the NC, then the NC had to be voided as well. I can't remember the details there too clearly...
One thing that strikes me immediately though: conferences can and do punish and void conference titles and achievements if it's determined that programs violate the rules. In 1965, it appears the ACC investigated and punished USC by voiding conference wins and revoking the co-championship from USC. The infractions I've read about thus far involved 3 FB players - one of which was on the freshman squad, and couldn't have played in any varsity games that season. The implication was $75-$100 in payments for meals and school books.
Then we read about the penalties that Clemson was found to be guilty of in the late 70s-early 80s. The listing of which was quite extensive and far more egregious than anything I've seen USC accused of in 1965.
But even though the ACC investigated Clemson like they did USC, and even though the ACC found Clemson guilty in violations that they added further penalties onto what the NCAA layed down - the ACC apparently allowed Clemson to keep their 1981 ACC conference title, while stripping USC of it's 1965 co-championship.
Another thing: I didn't like reading the article from The State, was all the vagueness and clouds regarding exactly WHAT the penalties were in 1965, and who committed them. All the coaches and players at the time seem to indicate that they all lived in a fog during that year, were never informed exactly WHY their achievement was being taken away, and didn't seem to really care or bother to find out why it was.
All kinda like, "hey we won a ACC title....oh, you're taking the title away from us and won't tell us why? OK, that's fine, cause we still won it anyways. We'll just move on".
That doesn't make any sense to me....