I think there are legitimate safety issues with refills, depending on the type of drink dispenser. Anything where you actually press your cup against a lever to activate the machine could easily involve transferring germs from your cup to the lever, and then back to whoever's cup uses the machine next. Less of an issue with something like the absolutely horrible Coke Freestyle machines -- the touchscreen has to be used regardless of whether it's a refill.
There are ways around that, though. There's a local QS restaurant near me that has a no refill policy, but only to existing cups. They will give you a new cup if you want more.
I wasn't sure if it was self server re-fill or if a employee has to do it. If it's an employee then the fix is easy, they throw away the empty you give them and use a fresh cup.