1. What kind of tangible evidence could be given for something so abstract? It would be impossible to prove what I thought of or felt 3 seconds ago for example, with the current available technology known to the common person.
2. If an occurrence is extremely frequent it is reasonable to not dismiss as coincidence. If everything is relational by cause and effect, then such frequent occurrences have a cause that may be harder for the common senses to detect.
3. To believe that everything is explainable to people in 'logical' terms assumes first, that humans are competent enough to explain the complex occurrences that happen to them. Many people myself included cannot explain everything they experience.
4. It is obvious people are not able to sense everything in existence acutely, therefore assuming what cannot be 'quantified' by basic senses does not exist, would be subtly entertaining the idea that humans only sense what does exist.
5. Because an occurrence does not provide an aftermath that is physically perceivable to the common person does not mean that it did not occur. Eg. I thought of the word bagel, but I cannot prove that with my resources, and I doubt scientists can.
Science is nice and has helped a lot but scientists usually dismiss these freakishly accurate coincidences with the alibi 'its just luck' a lot when those 5 points should all be taken into consideration. If man needs technology to detect a single celled amoeba then, it is reasonable to be open to the possibility they cannot detect an even greater subtlety which causes these 'phenomena' to occur, especially considering the limit of their physical senses compared to animals lower on the food chain.