Data-driven closures for large-eddy simulation (LES) are commonly designed to respect the symmetries of the Navier–Stokes equations, on the premise that this improves accuracy and generalization. We test this premise in a controlled comparison of three pointwise, Galilean-invariant closures built from the filtered velocity gradient: an unconstrained multi-layer perceptron, a group-convolutional network that is exactly equivariant under the 48-element octahedral group surviving discretization on a uniform grid, and a tensor-basis neural network. Trained on filtered DNS of forced three-dimensional turbulence, the three designs saturate to the same a priori and a posteriori accuracy as network size grows, and a direct conditional-mean estimate identifies this shared floor as the one-point optimal closure of Langford and Moser. Equivariance therefore buys parameter efficiency — the constrained models reach the floor with 25 times fewer parameters — but not a lower error floor. What does limit generalization is a blind spot shared with classical models: the scale-invariant normalization that makes learned closures robust also erases the Reynolds number, freezing their dissipation calibration at the training regime. The same symmetry analysis that constrains the architecture supplies the missing input — the filter-scale Reynolds number Re_Δ = Δ²‖∇ū‖/ν, the scaling-invariant combination the filtered equations single out. Closures trained across viscosities with Re_Δ as an extra input hold their calibration at held-out viscosities and filter widths, and partially correct it on an out-of-distribution Taylor–Green flow where Reynolds-blind closures mis-dissipate. Reynolds-number generalization in data-driven LES is thus largely a calibration problem, solved by the right theory-guided input feature.