Training foundation models is computationally intensive and often slow to converge. We introduce PIQL,Privileged Information for Quick and Quality Learning, the first framework to systematically integrate privileged information (PI) to simultaneously accelerate learning and improve generalization in tabular foundation models (TFMs). We construct two complementary forms of PI: (i) aggregate dataset-level statistics that reduce the burden on in-context learning, and (ii) encodings of the underlying data-generating program, providing knowledge beyond observable data. We further design an architecture that effectively transfers the train-time-only PI by learning to reconstruct it from observed context at inference. We provide a theoretical analysis characterizing conditions under which PI reduces the population-level approximation gap and accelerates convergence in finite-data regimes. Empirical evidence shows that PIQL enables TFMs to achieve faster convergence, lower final loss, and better generalization, in effect, reducing data and compute requirements. Our work establishes PI-guided pretraining as a principled and practical paradigm for improving the efficiency and performance of foundation models.