Search for imbalanced data here and on cross-validated. There is a lot of discussion on techniques, pros and cons.
Lets say it depends. But using "wrong" in the title may be too strong. Something may not be wrong but it may be non-optimal to your use case.
If the model is supposed to generate a well-calibrated probability, a down/up sample may effect the calibration. There are formulas and techniques that may be able to adjust, somewhat. If you do not care about a well-calibrated, then maybe no harm.
The model is losing information. This may be OK if the information is duplicated or all very much on one end of skewed data. But otherwise, the model may be weaker. Of course the model may be stronger if noise was eliminated or irrelevant records were eliminated.
Like you mentioned, the cut-off value may be applied wrong due to loss of information. Perhaps you are doing credit modeling and with the smaller sample, transaction amount became less relevant. But when the model moves into production and see the entire population for scoring, transaction amount is very relevant and the cut off value did not take that into enough consideration.
Or perhaps transaction amount became stronger in the sample and everything turns out better.
If you are interested in interpretation of the model - say coefficients of a logistic regression, then sampling often increases the standard error of the coefficients. If there are suppressors (partial correlation) weakening these may also weaken the coefficients or the model.
I am not sure what the free lunch is. If you down sample, there may or may not be an effect. There may or may not be an effect that you care about. But some work needs to be done there. Trading training time of the computer for analysis time of the human. But part of the analysis may be boot-strapping and comparing so perhaps no training time is eliminated.
You might want to state your goal and reason for down sampling. And read the imbalanced data posts since that may help focus the question.