* There are implicit assumptions in scientific studies ... Power calculations refer to the model and not to whether it is the correct model.*

True, but this crucial assumption needs to be kept in mind when using the study to inform yourself of the state of the world. Too often, it's forgotten that there are two questions that need answering for the study to be relevant and, only one of those has a number associated with it.

In that sense, Bayesian statistics, where this is explicit, are less misleading because they actually draw attention to the fact that we don't know that the model is correct.