"If the employee was not exempt but rather was hourly, and had some direction to go out on Saturday ' cuz the tickets cheaper, he should turn over the ticket to the bean counter along with the Saturday overtime slip."

You make an excellent point: the employer can't have it both ways. With the employees paying for the lodging on Saturday night and expenses prior to Sunday, the case to support the bean counter's claim that the vouchers should belong to the company is somewhere between extremely weak and non-existent. Along with the overtime slip, (if applicable), the employer would also be responsible for the Saturday night hotel bill, along with meals and incidental expenses from the time of departure onward. That was clearly not the understanding at the outset, so the vouchers belong to the employees.