Definitely an interesting first post. Whenever I get into discussions about this (usually with jealous Auburn fans), I fall back on the fact that there is basically the pre-WW2 era and the post.
After WW2, Bama has 10 AP national titles and 1 UPI national title. The only UPI title came in 1973, when UPI named its national champions prior to the bowl games. You might get some who quibble about the UPI title, but it was considered a legitimate source back then. Few reasonable people will really argue that point.
The problem comes prior to WW2, the time period which accounts for 5 national titles that Alabama claims. AP didn't begin naming a national champion until 1936. Alabama, of course, claims 1941, which is a matter of great debate among those who want to cast doubt about our national titles. There's probably some merit to the 1941 argument. However, the other titles claimed came before 1936, which means that a number of organizations were naming national champions. This is kind of the Wild West of the national title era, because so many teams could (probably legitimately) claim a title in this era.
The way I look at it, 11 of Alabama's claimed 16 national titles are not under dispute by reasonable people. And what makes this better is that those 11 titles came in the post-war era, meaning there were real football programs and a relatively modern game. If anyone wants to dispute the other five, that's fine. But if you're going to cast doubt on Alabama's early titles, you have to do the same for Notre Dame's three titles claimed before the AP poll. You have to do the same for Michigan, which claims EIGHT of its eleven national titles before the AP poll era. Treat everyone fairly and we still kick their ... in national titles. Roll Tide.