At the heart of the financial tug of war begun between college athletics and the gaming industry is a disagreement: Administrators say betting on college sports will increase the likelihood of scandals on campus. Gaming entities, armed with watchdogs, believe the opposite is true. What happened to Mike Hamrick in Las Vegas didn’t stay in Vegas. It stayed with him. One particular memory from his six years as UNLV’s athletic director — at the nexus of sports and gambling in the United States, with a sportsbook across the street from the football team’s practice facility — resurfaced recently. It was…