I was never stopped from using my own cup at the drink station, even thought there were always CMs around. I don't put the cup to the lever--I push the lever with my hand and a napkin, so I don't share my "cup" germs, and I don't get anyone else's cup germs either.
I measured (I was bored) My cup (refillable mug) will not quite hold a 12 oz drink and ice.