If you want a non-pejorative term that is used in academia/science for this kind of evidence, you could use case study. It's a common feature of, for example, medical, psychology, and business research literature. A definition from Merriam-Webster:
an intensive analysis of an individual unit (such as a person or community) stressing developmental factors in relation to environment
The "individual unit" is your "sample of one".
Note that case studies can be either qualitative or quantitative, depending on the method of inquiry into the particular case, though they may be especially popular among qualitative researchers (and may be denigrated by some more quantitative-focused researchers).