For every wise adage, there is an opposite and equally wise counterpart. "Fools rush in where wise men fear to tread" can be countered by "He who hesitates is lost." I bring this up because I am going to talk about the acceptability of acting on data from a scant sample, as in n=1. Big disclaimer up front: Don't do it all the time without careful consideration of the context. That having been said...
In qualitative research there is a phenomenon known as the "click of recognition" that the researcher can experience. In UX terms this means that sometimes we hear a user say something or see her do something and a light goes on. We have a clarifying moment or epiphany if you will. That is because in user research, the user is often a lens through which we see the application with our own preconceptions and biases filtered out. Something that seemed so crystal clear to us suddenly becomes vague or ambiguous when we see that same widget or paragraph through someone else's frame of reference.
How can you make decisions based on the input of just one user? Let me give some examples from a writing perspective. In doing so, I'm going to go through my "hierarchy of clicks."
Let's say I have written something, and I give it to my wife to look at. She sees a misspelled word and points it out. Do I say, "Thanks, but let me have twelve other people look at it too." No. It's wrong, I know it's wrong, I was just too close to it and didn't catch it. Little miss fresh eyes did, and I make the change based on an n of 1. The UI equivalent is a bug, or where I failed to apply a known and widely accepted best practice. It takes one user stumbling on it to trigger a click of recognition.
Now my wife keeps reading and comes across the sentence "Tom told Dick to fire Harry, and it made him mad." She makes the following observation, "I'm a bit confused about which of these characters you mean by 'him.' Was Tom mad because he had to tell Dick how to do his supervisor's job, was Dick mad because Tom was making him do the dirty work, or was Harry mad because he was getting fired?" Hmmm. Crystal clear to me when I wrote it because I knew whom I was referring to. Now that I have her lens, I can see how ambiguous (or triguous) the referent is. Do I need to get another opinion? Politics of marriage not withstanding, no. Now that I see someone else's reasonable take on it, I have a click of recognition.
But then she says, "Times New Roman is so boring, I think you ought to use Verdana." "Thanks," I reply while making a mental note to get twelve other opinions.