People often don't believe statistical conclusions if there isn't a graph of the data that clearly shows the same result, even (especially?) experienced statisticians.
Why is this? What is statistics for if we can't count on it to be reliably better than just staring at data?
The best hypothesis I have is that a graph is a way to integrate out degrees of freedom in the analysis. It lets you see whether any choices seem arbitrary, and whether different choices might have changed the result.
There's something deep to explore about how people with the most experience in a field often end up seeming like scientific nihilists to people on the outside. The root cause may just be that knowing things is extremely hard, and most things aren't true.