Does eating more veggies use more water?

I got an interesting question via "Ask the Conservationist" at work:
"Barbara Wimmel of Freiburg, Germany writes: As I have been a vegetarian for many years, one question has been on my mind for a long time. We are told incessantly to eat lots of fruit and vegetables: But isn't it true that (most? all? which?) vegetables can be grown only while needing a lot of water (and this often seems to mean irrigation)? If so what possible solution(s) exist for this problem?"

See the answer here: http://www.nature.org/science-in-action/science-features/ask-the-conservationist-october-2013.xml