Science is about replicable data. If it is only in your brain, then I can't learn from it and try to replicate it.
My anecdote regarding the three sisters is not science. But as a gardener, I don't tend to use science as a point of departure. Sometimes, and quite often, established science lets me see through the garbage, but then I do always have to remember that the value of a technique is not derived from the quality of someone else's description.
Anecdotes are a great jumping off point for scientific investigation, but further, they are crucial to establishing a network of shared experiences. Those experiences are the foundation of our regional gardening traditions, and those traditions are important to gardening as an art.
The point, for me at least, is to practice this art, as a subset of the art of living well. I make try to make use of all the arts and sciences and people I can find, paying closest attention to anecdotes, but always thinking in terms of broader theory. This organizes things in my head, and allows me to distill anecdotes into lessons, which are easy to store and recall, and can often be combined to make new personal discoveries or inspirations.
to be clear though, your definition of science is incomplete. I know I am a bit obsessive about words, but please put up with me. Semantics and etymology, and the hidden meanings and subtleties of words are a passion of mine. My work often involves the interpretation of texts from past eras, and it often makes me sad, because our language has lost its way. I believe the chief culprit is English hegemony. Speakers of related languages forced to learn English have an easier time connecting with the past, because so many words gain new dimensions, becoming living, breathing organisms possessing many dimensions and living not just in the moment.
I'll quote from wiki:
Science (from the Latin scientia, meaning "knowledge") is, in its broadest sense, any systematic knowledge-base or prescriptive practice that is capable of resulting in a correct prediction, or reliably-predictable type of outcome. In this sense, science may refer to a highly skilled technique, technology, or practice, from which a good deal of randomness in outcome has been removed.
(to put this in perspective, in modern usage, western boxing is called "the sweet science". It's not just a cute name, it's an appropriate description)
In its more restricted contemporary sense, science refers to a system of acquiring knowledge based on scientific method, and to the organized body of knowledge gained through such research.
The scientific method:
Scientific method refers to a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering observable, empirical and measurable evidence subject to specific principles of reasoning. A scientific method consists of the collection of data through observation and experimentation, and the formulation and testing of hypotheses.
and an interesting sidebar:
Karl Popper denied the existence of evidence and of scientific method. Popper holds that there is only one universal method, the negative method of trial and error. It covers not only all products of the human mind, including science, mathematics, philosophy, art and so on, but also the evolution of life. Beginning in the 1930s and with increased vigor after World War II, he argued that a hypothesis must be falsifiable and, following Peirce and others, that science would best progress using deductive reasoning as its primary emphasis, known as critical rationalism. His formulations of logical procedure helped to rein in excessive use of inductive speculation upon inductive speculation, and also strengthened the conceptual foundation for today's peer review procedures.
As for the three sisters approach, let's start with observation. What do we know about it? Who used it, for how long, and how successfully? What does that imply?