Why does water short out PCBs? (i.e. Why doesn't electricity follow the path of least resistance?)
Fallacy correction:   

"Electricity" NEVER 'follows the path of least resistance'.

Electricity is NOT like a single large Zorb bounding down a hillside. 

Electricity would be better modelled in this context as
a large reservoir of water being poured down a rough hillside.
Most of the water will follow major gullies and channels but some will find smaller side channels.

The question is not
"which path will the electricity follow?"
 but
 "how much current will flow along this given path?"

Low resistance paths will conduct higher currents.

Higher resistance paths will conduct less current.
 Only infinite resistance paths will conduct zero current.  

There are NO infinite resistance paths.

Plus:

When voltage is applied to water above a certain critical voltage, the water will decompose into Hydrogen and Oxygen - - known as "electrolysis". Any components in the water are liable to also decompose to produce eg Chlorine gas from chlorine products in the water. Even wholly pure deionised water can be decomposed in this manner.

Once you get even a small amount of current flow you get ions formed which promotes more current flow, lower resistance, more breakdown ... zap.

I have dropped a "pager" into sea water and a portable phone into concentrated chlorine solution* and "saved" both with no long term damage by immediately taking out the batteries and washing them in copious quantities of fresh water and then leaving them to dry completely (a very important step). And I have seen equipment destroyed by exposure to water with the batteries then left in.


Note to self: Remove portable phone from top pocket before stirring large bucket of Sodium Hypochlorite solution.

When splashing  along sea edge and generally having fun your pager should be in a salt-spray protected bag or, better still, left at home. 

Note to the young: Pager's were things we used to have before they invented cell phones. Effectively a receive only SMS system with no voice or any other features. Doctor's still seem to use them.