The way these risks are reported often makes this mistake. A statistically significant difference is reported as a "significant" difference, which means something different to lay people.
For example, if a change in diet increases the chances of getting a specific cancer from 1 in 1000 to 1.5 in 1000, that very well may be statistically significant. But, your odds of not getting that cancer go from 99.9% to 99.85%, which most people would not consider to be a meaningful difference.
For example, if a change in diet increases the chances of getting a specific cancer from 1 in 1000 to 1.5 in 1000, that very well may be statistically significant. But, your odds of not getting that cancer go from 99.9% to 99.85%, which most people would not consider to be a meaningful difference.