Like the stone tape theory, the basic idea of the water tape theory is that neighboring bodies of water absorb the emotional crisis energy of a traumatic event, imprinting the event in the body of water and spontaneously playing it back on repeat. While it seems possible the piezoelectric effect may be responsible for the attribution of mystical properties of crystals which may have lead to the foundation of the stone tape concept, the property of water memory is based solely on bad science.
Originally proposed by Jacques Benveniste in 1988, Benveniste, a proponent of homeopathy, sought to explain a foundational mechanism of the practice. In an experiment involving human antibodies being diluted out of existence in water, Benveniste reported that human basophils responded as if reacting to the actual antibodies.
He is quoted stating "It's like agitating a car key in the river, going miles downstream, extracting a few drops of water, and then starting one's car with the water."
It should be known that these results were only found in the solution that was violently shaken during dilution.
The Results were submitted to the scientific journal Nature and were the subject of some controversy. In the following issue, a follow-up investigation was conducted by Nature editor John Maddox and renowned skeptic James Randi. The results were found to be non repeatable, though Benveniste refused to retract the article stating that the protocol in the following investigations were not identical to his own.
Another proponent of magical water properties is Dr. Maseru Emoto who claims that thoughts or emotion can directly effect water droplets resulting in noticeable differences when the droplets are frozen, being deemed "beautiful" or "ugly". His methods and protocol are highly criticized, though Emoto openly admits that he is not a scientist.
There are countless other pseudoscientific claims revolving around water that I could rattle off, but they most likely wouldn't bring us any closer to the the origin of the water tape theory and it's relation to residual hauntings.
If I were to speculate, I would assume that it is merely a modification of the stone tape theory, bolstered by conformation bias. Being that water is even more abundant than quartz or limestone, finding a body of water near an alleged residual haunting if far more likely, creating an unfounded causal relationship between the two. This logical fallacy is know also as Post hoc ergo propter hoc (latin for after this, therefore because of this) and is nearly as abundant in the paranormal community as bodies of water and limestone are to tragic events.
Lets consider the concept. If water were capable of retaining the emotional energies produced by traumatic events, the world we live in would be cluttered by these projected playbacks. Water is run through all of our cities and houses through plumbing, there is water in the air, and the human body is 61.8% by weight. Think of it, we'd be sneezing ghosts!
This "theory", like most others attempting to describe the mechanisms of spirits, quickly falls apart with very little thought put to it. Let's continue to think before we "theorize".