Looking at the list of selectors for the national championships (1925, 1926, 1930, 1934, 1941, 1961,1964, 1965, 1973, 1978, 1979, 1992, 2009, 2011) that the University claims, it seems that the criteria for claiming a national championship for a particular season is that there were multiple selectors, at least one non-retroactive selector, or at least one of the major polls as a selector for that season. The NCAA in the past had a list of recognized national championship selectors for NCAA Div 1-A football and laying a claim to a national championship was as legitimate as the credibility that one wanted to assign to the selector(s) for that season.
The Houlgate System was one of the national championship selectors that was recognized by the NCAA. It is a mathematical system that retroactively awarded national championships for the seasons 1885, 1887 to 1905, and 1907 to 1926. It began awarding national championships annually after the bowl games in 1927. Thus, in 1941, it awarded Alabama the national championship after the Cotton Bowl win over Texas A&M.
From the seasons 1927 to 1935, the national championship awarded by the Houlgate System correlated with the majority of the other selectors (including retroactive selectors) 5 of 9 times (56% of the time). From 1936 to the last Houlgate awarded national championship in 1949, the system agreed with the AP poll 8 of 14 times (57%) of the time. So, the Houlgate system was in agreement with other selectors slightly more often than not.
I don't mind if rival fans are bothered by the University recognizing 1941 as a legitimate championship. The NCAA doesn't officially recognize ANY national championships for the sport of football in the FBS (Div. 1-A) and all the championships are primarily awarded on the basis of either a mathematical formula or the opinion of one or more people who typically are focused on only one, two or three local teams and give only a cursory glance at what other teams are doing. With the BCS, at least the two teams that are considered to be the best get to play each other. For most years in the AP and UPI system, it was unlikely that the two best teams would meet, so it was always just a guess as to which would prevail in a head-to-head matchup. I see no valid reason to consider an AP, UPI, or any other championship as more legitimate than the Houlgate System. There's a reason that the Div 1-A football championship has always been widely referred to as a "mythical" championship.
For those that are overly worried about what rival fans say about the championships that we claim, I welcome you to join me and just not give a rip about them. At least as long as we keep them busy whining about our championship claims, they don't have time to do more harmful things, such as trying to frame our recruits with violations.