As a former astronomer, one thing to highlight here is that statistical uncertainties aren't usually all that important in assessing how likely a result in astronomy is to be true. The main issue you grapple with in the field are your systematic uncertainties. When you report your uncertainty, it always is an uncertainty in the context of some model. However, if certain assumptions that your models have made are wrong, you will have underestimated your true uncertainty. Unfortunately, systematic uncertainties can't be reduced just by getting more data --- you have to somehow verify that the different assumptions your model has made are correct.

Astronomers spend a lot of time arguing with each other about whether they have properly incorporated all their systematic uncertainties. For measurements of dark energy this very quickly gets you into the weeds of Type Ia supernova physics (which is made more difficult because we don't know for certain what Type Ia supernovae are), stellar physics in Cepheids, the effect of metallicity, selection bias effects, and on and on.