One of the things that keeps beer-spoiling microbes at bay in finished beer is low pH. A pH of around (IIRC) 4.6 or less has a protective effect. This is one of the (many) reasons breweries care about wort and beer pH.
When you diluted your sample with water, you probably increased the pH to above this protective threshold. You also reduced any protective effect of the alcohol and added oxygen to the beer. In other words, you removed the safeguards against the growth of unwanted microbes.
There are no known pathogens that can survive in beer, but that applies to normal, finished beer. I suppose it's within the realm of possibility that you grew up an opportunistic pathogen in that bottle. That said, seems like that beer would have looked, smelled, or tasted odd if it was dangerous to drink. Were there any sensory indications that something was off with that bottle?