I realized a long time ago that I really enjoy drinking soda, and not much else. Very little interest in alcohol, sure I have some with friends but never when alone. Don't drink coffee (I have, of course, but never particularly enjoyed it or drank it regularly). I do enjoy Gatorade and fruit juice, of course it's because they are sweet.
Anyway, I also realized that if I'm going to drink soda regularly, I had to switch to diet. Just for the calories, really, at the time concerns about sugar weren't as prominent. But I gained a bit of weight in my late teens and switching to Diet Coke was a "free" reduction of 500 calories per day. "Free" as in, easy to switch, no dieting, no eating less, etc.
My point here is that I think the refill situation is the opposite of what you suggest -- diet soda doesn't cause me to drink more, it's the fact that I've always drank a lot of soda that caused me to choose diet soda.
Oh, and maybe it's related, I love chewing on ice that has been doused in soda. A server sees an "empty" glass and wants to clear it, but I see a mountain of delicious ice. Weird, I know.
e.g. This thing has no calories, therefore I feel justified in overindulging and drinking tons of it to let my primal urge for sweetness go unopposed.