Hmm. I'm not certain, but what I can say is that the cup holder had little springy "fingers" in it so that the soda can that I put in there was held in place and wouldn't move around. But I think there was more play in those fingers, so you could probably put something in there that was nearly the full diameter of that chrome opening.
But, perhaps somebody could drop by a store?
ddruz, what's a standard 3" water bottle? i.e., if I wanted to drop by 7-11 and grab a bottle to try, what should I look for? Myabe I can drop by Menlo Park on the way to work Friday.