I cannot see the deleted question, so I may be missing important context. One case that concerns me is equivocating confidence intervals with prediction intervals. The latter tends to be substantially less precise than the former.

A parameter such as a conditional mean of the patient outcomes may be very precise in terms of its confidence interval, but the spread in the outcome variable could be quite wide nonetheless. Ignoring how wide the prediction interval is in assessing risk to patients could be disastrous.