From what I found, the career numbers do not support your position;
McBee 2010-11 .882, 11-12 .839, 12-13 .840
Golden 2011-12 .828, 12-13 .778
McRae 2011-12 .759, 12-13 .771
McBee's worst season at the line was better than anybody else's best season at UT during that era.
When the other team is looking to foul at the end of the game when they are trailing, then any perceived lack of foot speed should result in one being easier to foul instead of harder to foul.
If he wasn't shooting foul shots at the end of the game it was probably because the other coach said "don't foul the dude with the crazy mustache" since they pay attention to statistics. Or if Colban is coaching "don't foul the token whitey".
Your position doesn't match up to the facts.