My point is that it's very easy to check "model calibration" (eg. "Plug values from outside data"). Just run the code with different values.
Because it's so easy to check those things (assuming the data is not proprietary or whatnot) I'd argue it's a much lesser problem than the "garden of forking paths" in lab experiments where it's much harder to test robustness of the result.
Moreover, I don't think anyone intelligent is foolish enough to take the coefficients in an econometric study literally; at least I would hope not.
You should start with 'calibration' in economics. No, it is not quite what you (seem to) think it is. No, it is not quite "the same type of thing" as p-hacking and low-powered studies in psychology. (Whose poor reliability, by the way, is almost common knowledge by now.)
Look it up, and see how the sausage is made.