Can statistics help to definitively deduce causality? RCTs require that you state the set of variables that you believe influence a given outcome of interest, a priori, therefore if one wants to understand the effect of a treatment/intervention, the typical procedure would be to model the intervention distribution based on the variables which act on the intervention, however, if the variables which you have listed a priori is not definitive, then the effect would be biased.
There are a few other well-known methods for establishing causality, for example, the Bradford Hill guideline in Epidemiology is not entirely empirical since it is based on assumptions that can vary depending on the dataset that is gathered, for example, an assumption is that the effect size is greater than that of its confounders but since confounders are exogenous, then its effect can never be known.