I had this same conversation just this morning!
Somehow I doubt the full humor of the situation will be apparent to most people, but this conversation occurs at my job on an occasional basis. A sample size of N=3 is a barest minimum for even a t-test, and on that basis alone probably isn't enough, but I'm willing to set that aside for the bigger issue, because it depends on the question.
It is a matter of the question asked. Not all experiments are the same, nor are all samples the same. In my conversation this morning, there was a basic misunderstanding of the sample unit. There was a sample size of N=3 in one group (treatment), and another group of 3 serving as a control. The problem (well one of the problems) was that the controls were not used as an independent group, but rather as a way to normalize each of the first 3. Instead of having two groups of 3 each, that we really had was a single group of 3 pairs of subjects (matched pairs). This lead to a few hours of trying to untangle What had been done versus what needed to be done. Frustrating, but then education is an important part of my job too.