If you want to say that when you do a frequentist analysis which doesn’t include any concept of prior you get a result that has a similar form to the result of a completely different conceptually Bayesian analysis which uses a flat prior (definitely not “a point distribution derived empirically”) that may be correct. It remains true that there is no prior in the frequentist analysis because they are not part of frequentist inference at all.
Priors are not used in construction of frequentist approaches, but that does not mean that the analyses aren't isomorphic in theory.
Point distribution <=> point estimate as a sample from an initially flat distribution. A priori vs a posteriori perspectives, which are equivocal if we are to take your description of frequentist statistics into account ;)
It’s not my description of frequentist statistics. It’s the frequentist statisticians’ description. This is from Wasserman’s All of Statistics:
The statistical methods that we have discussed so far are known as frequentist (or classical) methods. The frequentist point of view is based on the following postulates:
F1 […]
F2 Parameters are fixed, unknown constants. Because they are not fluctuating, no useful probability statements can be made about parameters.
