We are not saying that statisticians should not tell stories. Story-telling is one of our responsibilities. What we want to see is a clear delineation of what is data-driven and what is theory (i.e., assumptions).
The standard claim is that the observed effect is so large as to obviate the need for having a representative sample. Sorry – the bad news is that a huge effect for a tiny non-random segment of a large population can coexist with no effect for the entire population.
That last one is an appropriate response to the Freshman Fallacy.