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Multi-fidelity machine learning has become a cornerstone of computational materials science because it leverages inexpensive low-fidelity data to accelerate training while reserving costly high-fidelity density functional theory (DFT) calculations for final refinement. Yet an often-overlooked source of uncertainty remains: DFT itself is noisy. Different choices of exchange-correlation functional, basis-set completeness, pseudopotential construction, and numerical convergence criteria introduce systematic and material-dependent errors that are routinely treated as exact labels. This theoretical analysis develops a unified conceptual framework for tracing how DFT error propagates through multi-fidelity training pipelines and ultimately inflates the variance of machine-learned predictions. The framework is grounded in recent theoretical and review literature on Gaussian-process and neural-network potentials, uncertainty quantification, and multi-fidelity surrogates. Proof sketches demonstrate the conditions under which multi-fidelity architectures reduce propagated variance and those under which they amplify it. Practical implications are drawn for uncertainty quantification protocols, optimal fidelity weighting, and the design of future multi-fidelity benchmarks. By making the DFT-to-ML noise pathway explicit, this work supplies a rigorous conceptual foundation for trustworthy data-driven materials modeling and highlights the necessity of reporting total (not merely model) uncertainty in high-stakes applications.