I actually enjoy brewing beer in my spare time. You're right in that it is a lot of water in beer, but if you had a contamination of bacteria in an early batch you would get the problem of the bacteria competing with the yeast. If the contamination is introduced after a certain point of fermentation, newly introduced bacteria would no longer get a hold because of the alcohol levels.

So in short, you are correct in that if you start brewing with contaminated water you will get the same problem in the end product.