Let's just see...of those 12, according to Wiki:
1925 - OK
1926-OK
1930 - OK
1934 - OK
1941 - Went 8-2, Number 20 in the AP, lost to Miss St & Vandy, selected national champs by Football Thesaurus. (shouldnt claim this one)
1961 - OK
1964- This one belongs to Arkansas - Alabama lost their bown game to Texas, but was awarded the NC BEFORE the bowl game. (shouldnt claim this one, Arkansas does)
1965 - OK
1973 - Again, lost to Notre Dame in the last game of season, selected NC's by Coaches Poll, shouldnt claim this one. Because of controversy, the polls started waiting until after the bowls.
1978 - OK
1979 - OK
1992 - OK
So, at least 3 shouldnt count.
The number of those that do count is impressive, however.