"Statistically significant results" mean that there's a 5% chance that results are wrong in addition to chance that the wrong thing was measures, chance that sample was biased, chance that measurement instruments were biased, chance that mistakes were made during analysis, chance that publication bias skewed results, chance that results were entirely made up and so on.
"Not statistically significant results" mean all those, except chance of randomly mistaken results even if everything was ran correct is not 5%, but something else, unknown, and dependent of strength of the effect measured (if the effect is weak, you can have study where chance of false negative is over 99%).
So results being statistically significant or not, is really not that useful.
For example, here's a survey of civic knowledge. Plus or minus 3% measurement error? Not this time, they just completely made up the results.
Take home exercise - what do you estimate Bayesian chance of published results being wrong to be?