Multi-fidelity Bayesian optimization (MFBO) is a powerful approach that uses low-fidelity, inexpensive sources to speed up the exploration and exploitation of a high-fidelity underlying function. Many existing MFBO methods with theoretical support rely on strong assumptions about the relationships between different fidelity sources to build surrogate models and guide exploration using low-fidelity sources. However, in practice, these assumptions can result in model misspecification, leading to less efficient exploration than expected. To address these issues, we propose a random-sampling and partition-based MFBO framework that is robust against cross-fidelity model misspecification. Our results demonstrate that this algorithm effectively handles complex cross-fidelity relationships and achieves efficient optimization of the target fidelity.