What about the process made it "safer"? Was it because of the bacteria destroying nature of the alcohol or because of the distillation or pasteurization process?
More importantly, would they have ACTUALLY understood that this was killing harmful bacteria or is it something we miss-attribute in retrospect and they just were lucky boozehounds?
EDIT: Thank you for the responses and I apologize for the grammar in the title... really wish you could edit those bad boys.
This has often been one of those questions that makes me get all, "Hulk Smash!"
We have evidence as far back as Roman times that Europeans knew how to recognize safe water sources over bad as evidenced by writers such as Frontinus and Vetruvius. Hippocrates advocated boiling water around 300 B.C. to remove impurities, and this knowledge would not have been lost in Medieval times.
People of the Indian subcontinent were even filtering water through a system very similar to modern municipal fine particulate filtration (larger aggregate down to fine sand filtration).
As idjet has stated, this is one of those enduring myths that refuses to die the death it deserves for it's lack of common sense and historical basis in fact.
This 'anecdote' is based on bad history in several respects: on the question of clean water (there was generally plenty), on the bacteria-killing effectiveness of alcohol content (not likely much, too low content), on the likelihood of pasteurization's same effectiveness (unlikely pasteurization occurred as a standard practice), and the constant drunken state of medieval peoples (absence of proof).
The above have been discussed here quite thoroughly. The FAQ has lots of the threads, here are medieval-oriented discussions: How did people (esp. European townsmen) get their fresh water? and How drunk were the people of medieval Europe? (see further discussion here)
/u/Qweniden and I had a pretty good discussion about alcohol in the British navy here, if it's interest to you:
I bring it up because the anecdote you reference gets extended to sailing: "sailors drank rum because the water was so bad," etc.
Other than incidences of some Brewery workers being spared by cholera outbreaks in the 17-1800s (because they had a separate water supply that wasn't contaminated with sewage, and that they mostly drank the spare ales they brewed) I can't think of any specific incidences of Alcohol being used as an alternative to clean water.
The alcohol content needed to behave as an antiseptic would not be found in all but the strongest of non-distilled beverages. Even then the heavy sugar content of Ales and Wine and Meads would be fuel for many pathogens.
Boiling water is hardly rocket science and had been common practice since the well before the Roman Empire. While a lot of knowledge and civilisation was lost after the fall of the Empire (glassworking, architecture etc) boiling water wasn't something so esoteric as to be lost by the fall of an Empire.