Real-world MRI reconstruction systems face the open-world challenge: test data from unseen imaging centers, anatomical structures, or acquisition protocols can differ drastically from training data, causing severe performance degradation. Existing methods struggle with this challenge. To address this, we propose BiasRecon, a bias-calibrated adaptation framework grounded in the minimal intervention principle: preserve what transfers, calibrate what does not. Concretely, BiasRecon formulates open-world adaptation as an alternating optimization framework that jointly optimizes three components: (1) frequency-guided prior calibration that introduces layer-wise calibration variables to selectively modulate frequency-specific features of the pre-trained score network via self-supervised k-space signals, (2) score-based denoising that leverages the calibrated generative prior for high-fidelity image reconstruction, and (3) adaptive regularization that employs Stein's Unbiased Risk Estimator to dynamically balance the prior-measurement trade-off, matching test-time noise characteristics without requiring ground truth. By intervening minimally and precisely through this alternating scheme, BiasRecon achieves robust adaptation with fewer than 100 tunable parameters. Extensive experiments across four datasets demonstrate state-of-the-art performance on open-world reconstruction tasks.