I don't think his argument was that MTSU is a better school than Vandy or vice versa.
He did after all state that folks who get a law degree from Vandy will certainly get higher pay than from lesser schools.
However, I do understand the point that certain degrees from so called "lesser schools" can and do mean more than equivalent degrees from Vandy. In this case it isn't about saying "Hey I went to Vandy" because that might not mean much if the department that it is in is not very good.
Case in point. I was offered a chance to go to Vandy when I graduated high school but I chose to go to UT. Why? Because UT has the better Anthropology department which is what I'm interested in. Does Vandy have an anthropology department? Yes but it is focused highly on archaeology and not physical, I could still get an education on physical anthropology at Vandy but it would not be nearly as complete as one at UT. Therefore, since I wanted to pursue my masters and my doctorate, it was in my better interest to go to the "lesser" school that had the better program, UT.
So when it was time to apply to my master's program, it is far more impressive that I was a volunteer at the body farm and conducted research with the donated collection at UT, then it would be sitting in lecture halls at Vandy. I did go on a field school through Vandy, but that was archaeological and not physical anthropology, again not as helpful for my career.
I know this is just my own personal example but it is a valid point that depending on the degree and the program, so called "lesser" schools can be more valuable than the "higher education" ones.