Just depends on what you want to claim. We have more than 12 awarded by various organizations down through the years.Generally we show 12, the NCAA of course does not recognize an official division 1 NC.
Of the oldest ones, there was a time when the Rose Bowl was the premier bowl game by a long way, and its winner was recognized by most as the national champ. Various organizations or respected sports peope recognized them as well. that is the basis for those shown in the twenties and thirties. The one on 1942 is pretty suspect, and if it were me I would not show it. 1961 is clear, as we were undefeated and ranked #1 in the polls. The first controversial year is 1964. One of the polls, the AP, I believe, decided to close its polls before the bowls, and our undefeated team was given its NC. The otehr poll waited until afterwards. Since we lost to Texas in the Orange Bowl we didn't get that half of the NC, but it is certainly legitimate to claim one that one of the two major selecting organizations awarded us.
Im 1965 we were 8-1-1 going into the bowls and ranked fourth. The AP decided to wait until after the bowls, to avoid what happened in 1964. Well two of the teams ranked ahead of us lost, and we hammered the third one in the Orange bowl, so at the end of the day we were voted number one.
In 1966 we were undefeated and a two time defending national champion, but the pollsters were determined we would not get the third one in a row (the best team of the three IMO) so they voted Michigan State and Notre Dame (who had played to a tie ) ahead of us. We could claim that one on our list, but we don't, just honor that team as "The uncrowned champions".
In 1973 we were undefeated in regular season play but lost the bowl game. We were awarded the NC by an organization that picked before the bowl game.
In 1975 we were 10-1 going into the bowl games, won ours, everyone ahead of us lost, but we were "leap frogged" in the final poll. We could easily claim one that year. 1977 was pretty much a repeat of 1975 and we could claim that one as well.
In 1978 we had an early loss to USC, then ran the table. USC picked up a loss later on, and as I remember this year the two major polls were split at the end. I certainly don't feel bad about claiming that one.
In 1979 we ran the table and were unanimous national champs.
In 1992 we were unanimous national champs.
So I'd have no problems with 11 of the 12 we show, and I'd add 1966, 1975 and 1977.
The blogger did not mention that the Barn's lone NC was 1957, and that it was a split one because they were on probation for recruiting violations and the coaches poll refused to consider them. Their 1958 was also undefeated (one tie) but also on probation. Srangely, 35 years later they ran the table but were not considered for the NC because (guess what) they were on probation. I sympathize with them for 2004, we've certainly been there.
