Ambiguity of anaphoric reference is the problem here.
Take out the "flagship" and the quote is just an innocuous, feel good kind of thing. But he did say flagship, intentionally we assume, so things get more complicated.
To what earlier idea does Freeze's use of "that" in the last sentence refer to in the quote? Does the "that" point to the fact that both players come from out of state? Does it mean that these two players can empathize with each other about having to learn the customs of their new surroundings? I could go with that; empathy leads to shared understanding and common interests, which leads to mutual love and respect, etc.
The ****** up part of the quote is Freeze's use of the word "flagship". As others have noted, we assume that it must be there for a reason, and as we continue reading, looking for that reason, we reach the "that" line. Now we are faced with interpreting the "that" to refer not to the fact that these players love each other because they are on the same team, or share the common bond of being teammates despite being from different places, NO, we are left with the claim that the reason they love each other is because they are at the "flagship" institution in the state of Mississippi. And THAT makes him sound like a douche.
edit: okay, I went and watched the speech at the link posted, and it is a different context and the first part of the quote is a bad paraphrase, but the flagship part is there pretty much verbatim, so point still stands. But wow, that speech was weird, about half way through it it veers off into a recruiting speech about how much better next years players are gonna be than the guys he is standing in front of and trying to fire up. Just imagine last year's post-game speech as a pre-game motivational talk and you pretty much have it.