Overfitting is one of the most persistent challenges in automated program repair (APR), typically attributed to weak or incomplete test suites. In this paper, we take a different view: overfitting is not just a nuisance but a fundamental consequence of undecidability. When full specifications are unavailable, test suites serve only as partial correctness oracles. As a result, overfitting emerges as a structural outcome rather than an incidental defect. This perspective reframes overfitting not as a solvable bug in APR, but as an inherent boundary of the problem itself. We discuss the implications of this shift and call for a research agenda that works within these limits, developing methods to quantify, explain, and ultimately reason about overfitting as an unavoidable aspect of repair.