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Feature disentanglement on a frozen vision foundation model is an appealing recipe for unified, multi domain visual anomaly detectors in manufacturing inspection: separate a domain-invariant representation z_inv from a domain-specific one z_dom, and detect on z_inv, assuming that enforcing statistical independence improves out-of-domain defect detection. We test this assumption directly and report a clean negative result. On a frozen DINOv2-L backbone we add a Hilbert–Schmidt Independence Criterion (HSIC) penalty and sweep its weight λ over five seeds on the public MVTec-AD and VisA benchmarks. (i) Independence is learned but does not transfer: in-domain CKA(z_inv, z_dom) drops 0.896→0.093, yet the same weights yield 0.82–0.93 on a new dataset. (ii) Increasing λ never improves image AUROC and, when strong, gives a small (practically negligible) but significant decrease (paired t = −4.09/−6.61, p<0.05)—an outcome the detector geometry partly pre-determines, since the PaDiM detector is invariant to invertible linear reparameterizations of z_inv and can respond only to changes of the learned subspace itself. (iii) An apparent “+7.7-pt” gain over a pooling-unmatched frozen baseline is shown to be a pooling-kernel artifact. We distill a measurement-control checklist and release a reproduction package; scope is limited to frozen DINOv2-L + a linear head + PaDiM on MVTec→VisA.