OK, Maybe this isn't the right thread to ask this, but why won't those players in Memphis go to TN? Just curious.
I will try to answer your question based on my experiences East Tennessee as a whole and Knoxville over the past 20+ years. People usually want to be in an environment where they feel comfortable. As an urban city, Birmingham is very similar to Memphis and is only 45 minutes away from T-town. So, those players have somewhere they can get to quickly that is somewhat familiar to them. No such place near Knoxville.
As a black non-athlete, I felt very included during my 4 years at BAMA. Those were some of the best years of my life and I am 40+ years old. Many black students who were not athletes and some that were that I have known over the years that attended UT don't come away with the same warm fuzzy feeling about their alma mater that I have about mine. Many went because they could not afford out of state tuition and they don't have any association with UT after they graduate.
A major factor that Memphis, Birmingham and University of Alabama have in common is the Civil Rights Movement. I think those events had a positive impact on the future of those places. Those cities and the University are better because of their past and the effort that they put forth to change. East Tennessee for the most part stayed as far away from those issues as possible on purpose.
Here is an example from an UT football standpoint. UT named a street after Peyton Manning before he left. There street is Manning Way (I believe). When UT won the National Championship in 1998 with Tee Martin as the QB. Since the precedent had been set, it was assumed that the QB that led you to your 1st championship in the modern era would get a street, too. When asked about it, UT's response was something to the effect of, "we can't go around naming streets after every good UT player, we will run out of streets". They may have eventually named a street or something for Tee but that first response stays with you. Many UT fans up here will tell you today that Manning paved the way for Tee Martin to win the championship.
The families of the players in Memphis hear this kind of stuff and remember it as well as their past experiences in East Tennessee.
When I was living in East Tennessee, the Tennesseans commonly referred to Memphis as "The largest city in Mississippi." Perhaps that attitude partially explains the failure of UT to attract blacks from the extreme west.
You are absolutely correct that the people in East TN don't consider Memphis as a part of TN. It's like Memphis is a small territory separate from the rest of the state.
The real problem is geography. Memphis is farther from K-Town than to T-Town and far, far closer to OM. I haven't Mapquested or Googled it, but Fayetteville may even be closer. "State Flagship School" only goes so far. The further kids are away, the looser the ties to the state school. It's just the way it works. However, I believe that, even when you take the kids who leave TN and add them to the ones who sign with some TN school, the total number is going to be pretty disappointing...
I think another problem is that many kids in the Memphis area, particularly the black ones, probably don't grow up dreaming of being a UT Vol. In AL, usually kids pick early in life either BAMA or Auburn. This goes back to your argument that pee wee and high school football in TN is just not the same quality as AL and GA, never mind FL or TX. The passion is just not the same.