Gaussian Process (GP)-based Bayesian optimization (BO), i.e., GP-BO, emerges as a prevailing model-based framework for DBMS (Database Management System) auto-tuning. However, recent work shows GP-BO-based DBMS auto-tuners are significantly outperformed by auto-tuners based on SMAC, which features random forest surrogate models; such results motivate us to rethink and investigate the limitations of GP-BO in auto-tuner design. We find that the fundamental assumptions of GP-BO are widely violated when modeling and optimizing DBMS performance, while tree-ensemble-BOs (e.g., SMAC) can avoid the assumption pitfalls and deliver improved tuning efficiency and effectiveness. Moreover, we argue that existing tree-ensemble-BOs restrict further advancement in DBMS auto-tuning. First, existing tree-ensemble-BOs can only achieve distribution-free point estimates, but still impose unrealistic distributional assumptions on uncertainty (interval) estimates, which can compromise surrogate modeling and distort the acquisition function. Second, recent advances in (ensemble) gradient boosting, which can further enhance surrogate modeling against vanilla GP and random forest counterparts, have rarely been applied in optimizing DBMS auto-tuners. To address these issues, we propose a novel model-based DBMS auto-tuner, Centrum . Centrum achieves and improves distribution-free point and interval estimation in surrogate modeling with a two-phase learning procedure of stochastic gradient boosting ensembles (SGBE). Moreover, Centrum adopts a generalized SGBE-estimated locally-adaptive conformal prediction to facilitate a distribution-free interval (uncertainty) estimation and acquisition function. To our knowledge, Centrum is the first auto-tuner that realizes distribution-freeness to stress and enhance BO's practicality in DBMS auto-tuning, and the first to seamlessly fuse gradient boosting ensembles and conformal inference in BO. Extensive physical and simulation experiments on two DBMSs and three workloads show that Centrum outperforms 21 state-of-the-art (SOTA) DBMS auto-tuners based on BO with GP, random forest, gradient boosting, OOB (Out-Of-Bag) conformal ensemble and other surrogates, as well as that based on reinforcement learning and genetic algorithms.