I think only Vandy has an overall higher minority %, and they don't really count.
Florida is the most diverse, only 59% white. MSU is 72% white.
I think MSU has the highest African American percentage (around 23%), but Florida is the most diverse. They're about 20% Latino, 8% African American, and 8% Asian.
For the record, we aren't far behind you at 75% white and 15% African American.
So the statement should be that MSU has the largest African American population in the SEC, not that it's the most diverse.
ETA: Vanderbilt is 64% white, about 9% Asian, 9% African American, and 8% Latino.
Those percentages don't count mixed race, unknown, American Indian, or Pacific Islander. Those are the primary ones that make up the difference for those schools, but they're small enough numbers I didn't show them.
So if you're using the definition of lowest percentage of majority, State is not the most diverse. Edited to include the actual white percentages at each SEC school:
1. Florida - 59.1%
2. Vanderbilt - 64.1%
3. Texas A&M - 68.8%
4. MSU - 71.6%
5. Georgia - 73.9%
6. Ole Miss - 75.3%
7T. South Carolina - 78.0%
7T. LSU - 78.0%
9. Kentucky - 79.9%
10. Alabama - 80.9%
11. Arkansas - 81.0%
12. Tennessee - 81.8%
13. Missouri - 82.1%
14. Auburn - 86.0%
As an aside, this only counts the main campuses for each. Auburn's number really surprised me. I expected Arkansas, Missouri, and Tennessee to be near the bottom, as those states don't house much in the way of minority populations other than spots in urban centers like Memphis or St. Louis.
But by that measure, MSU is the 4th most diverse.
My source was collegedata.com. I'm sure the numbers might be slightly different depending on where you find them, but I think those numbers are largely accurate.