Objective. Privacy regulation constrains sharing line-level electronic health records (EHR) across institutions. One alternative is to aggregate counts into a cube, a table of counts for every combination of categorical variables, with cells below a threshold suppressed. This study asked whether common analyses on the cube reproduce conclusions from line-level data, and whether suppression prevents recovery of the small cells it is meant to hide. Materials and Methods. A Bayesian count-inference pipeline was built that reconstructs suppressed counts and doubles as a reconstruction attack. Applied to 285 pediatric kidney-transplant patients at Boston Children's Hospital, statistical fidelity (Jensen-Shannon divergence, Cramer's V, and R2) and analytical utility (marginal distributions, subgroup graft rejection odds ratios, and logistic-regression classification) were evaluated. Conditional Tabular GAN (CTGAN) synthetic data served as a comparator. Results. Statistical analyses on the cube recapitulated results from line-level data. Across 106 demographic-by-medication subgroups, a bootstrap mean of 3.5 subgroups showed a significant graft-rejection association. The cube's odds-ratio sign changes reversed no significant associations, versus 2.3 for CTGAN. The same reconstruction also defeated suppression: in a 10-variable cube, 76.6% of suppressed cube cells were recovered exactly (14,554 of 18,994), including 85.5% of single-patient cells. Discussion. The cube reproduced common kidney-transplant analyses, but the same reconstruction also recovered suppressed cells; fidelity and privacy risk are thus two faces of one reconstruction rather than independent properties. Conclusions. The cube is a useful surrogate for these kidney-transplant analyses only when paired with a stronger privacy mechanism. This study demonstrated reconstructability of suppressed counts, not re-identification.