It may be truth, but it is not evidence.
—Thomas H. Huxley

Several years ago I saw part of a documentary on extra-sensory perception (ESP) in animals. One of the cases put forward as evidence was one in where a dog had been responsible for rescuing a drowning person. According to the dramatization of the event. the victim, who was mute and possibly confined to a wheelchair (in any event could not swim), had fallen into a river. The river was flowing fast and noisily at the time. As the victim struggled in the river, unable to cry out for help being mute, they were swept downstream and around a bend or two. Now downstream was another human (I do not remember the sex of either this person or the victim). This person had been walking along the river with their dog and had turned and headed back to their car. Having gotten some little distance from the river, the dog turned and went back to the victim’s rescue. I do not remember whether the dog actually rescued the victim or drew its owner’s attention to the victim, who then effected the rescue. I remember something about the dog’s excited barking at something in the water getting the owner’s attention.

The gist of the argument is that the river was noisy so the dog could not hear the splashing of the struggling victim over the river noise, the human victim was mute and couldn’t call for help, and the dog was walking away from the river and couldn’t see the victim or the river. The dog’s owner neither heard nor saw anything so the dog could not have either. The victim, being mute, was unable to call out, however due to the  extraordinary peril of the situation, sent out psychic cries for help that the dog picked up. If you believe in ESP this is evidence for its existence. But is it “scientific” evidence? No, it isn’t. Now I am not saying that ESP doesn’t exist. It may exist and ESP may have been involved in this instance. But this is not “scientific” proof of ESP. There are other explanations, explanations that don’t involve ESP, that have to be ruled out first. When an anecdote “supports” what you believe we tend not to examine it closely, these are precisely the ones that need to be closely examined.

Sherlock Holmes is reputed to have said that after you have ruled out all other explanations whatever is left, no matter how improbable, must be the truth. This is a good working method and the scientific method in a nutshell. By experimentation (controlling variables, changing only one thing at a time) you can rule out possible answers and what is left is probably the correct answer.

The anecdote related above doesn’t rule all other possible solutions. Contrary to your opinion it does not rule out the dog having heard or seen the victim struggling in the water. We have the dog’s owner statement that the dog could not have heard or seen anything. That’s based on the owner’s perception, nobody asked the dog. (Of course nobody asked the dog, we don’t know how to ask the question or probably understand the answer.) What the owner recalls seeing, hearing, not seeing, or not hearing is irrelevant to what the dog may have or not have seen or heard. Anyone who has used or heard (actually you do not hear) a dog whistle knows that a dog’s hearing exceeds the range of a human’s. Also a dog’s visual field is wider than a human’s. Their eye’s field of view extends further to the side and back of a than a human’s. Perhaps the dog saw something out of the corner of its eye. Because the owner didn’t see anything doesn’t mean the dog didn’t.

There is one further factor to be considered. Based on my personal observations, and what I have been told, and observed, most humans are not very aware of the world around themselves. Their senses may function very well but a lot of what their senses pick up never reaches the conscious level of the brain. I may have a very low opinion of the awareness of humans of their surroundings. However, based on the frequency with which I drive up behind people sauntering down the middle of the parking lot blissfully unaware that I am behind them. They always have such a surprised look on their faces when after 5 or 10 seconds they look back and see my truck. Humans who live in cities and/or suburbia seem to have lost at least some of that “situational awareness” we must have had long ago. Some still have and I believe, so do domesticated dogs and cats.

Nothing was offered in the documentary as evidence that the dog could not have seen or heard anything, nothing but that its owner was not aware of anything. I have spent a number of nights camped along creeks or rivers. I know that there is a rhythm, a pattern to the noise flowing water makes. Each piece of river has its own rhythm, depending on the configuration of the river bed and the amount of water in it. I have heard, among that pattern, the added sound of a deer stepping into the water. It is quite possible that the dog heard the different noise of the human victim struggling in the water. This possible explanation was not ruled out. Further, the possibility that the dog had looked back was not ruled out. There are at least two non-ESP explanations that have not been excluded. ESP may have been involved but this is not, scientifically, evidence for it.

Anecdotal evidence is usually not scientific evidence, the variables are not controlled. It may however point to interesting research topics. Hunters, explorers, and others in Africa occasionally reported incidents of elephants moving leisurely along in one direction, pausing as if listening to something, then heading off in a different direction. Following the elephants (best done at a discrete distance) they were seen to meet another herd of elephants coming toward them. There other similar cases where elephants seemed to be aware of the presence of other elephants miles away, who they were, and what they were up to. Hunters had known for years that a contented elephant’s stomach rumbled. If it stopped you were in for trouble. (The “rumble” isn’t stomach noises and is under conscious control.) Eventually it was discovered (by Katy Paine, etc.) that they were in fact communicating by subsonic vibrations transmitted through the ground (and felt through their feet) and through the air.

While anecdotal evidence may not be considered suitable evidence to support a hypothesis, when a categorical statement is made (such as: all swans are white), anecdotal evidence may be legitimate evidence against it (such as: I have seen black swans in Australia).