As for being able to "safely disregard" it... an insufficient number of data points doesn't mean that at all. It means you can't draw conclusions one way or another.
Let's put it this way: your team has a new chemical that's supposed to do (amazing thing). You decide to test it on yourselves. The first guy takes it and dies instantly.
Do you then say "Hey, 'n=1', so I can 'safely disregard' the fact that Dave just keeled over." and take it yourself?
I think not.
To be clear here, I think the COVID-19 vaccines deployed in the United States are both safe and effective -- but the solution to bad statistical reasoning is not even worse statistical reasoning.