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Causal-model arguments establish that a classical causal model reproducing Bell correlations while exhibiting no-signalling must be unfaithful: its no-signalling independences are not entailed by d-separation in the causal graph. Applied to time-symmetric, retrocausal, and all-at-once models, this is the fine-tuning objection. The resulting debate has largely concerned whether faithfulness is the appropriate norm, without a criterion for deciding particular cases or an associated measurement.This paper supplies a proposed criterion and establishes a precise symmetry result for the balanced binary singlet sector. If a nonnegative \(2\times2\) compatibility table has the simultaneous-outcome-flip symmetry \[ m_{++}=m_{--}, \qquad m_{+-}=m_{-+}, \] then every common scalar entrywise map \[ m_{xy}\longmapsto f(m_{xy}) \] with nonnegative output and nonzero normalization preserves uniform local marginals. No monotonicity, continuity, differentiability, or power-law assumption is required. Within two-qubit quantum kinematics with ideal analyzer projectors, joint rotational invariance and perfect same-axis anticorrelation force the singlet state and hence this pairing symmetry. The theorem establishes robustness relative to the symmetry-restricted deformation class; it does not confer causal faithfulness or robustness against arbitrary symmetry-breaking cellwise perturbations.The same singlet-plus-common-map structure has a deformation-independent surplus consequence: \[ E^f(\pi-\Delta)=-E^f(\Delta), \qquad E^f(\pi/2)=0. \] These angular identities are distinct from no-signalling and can fail experimentally. They provide the surplus consequence required by the proposed criterion in the balanced sector.A separate constant-flux completion law predicts an exactly flat ideal joint completion rate. We compare it with a Bell-local sign--cosine model followed by a joint two-bin selection rule. The pointwise maximal acceptance envelope for reproducing the singlet correlator has symmetric minima \[ Z^\ast\simeq0.878567 \] near \(46.44^\circ\) and \(133.56^\circ\). A flat calibrated joint acceptance rate above this value excludes that two-bin class. More generally, total variation gives \[ S_{\mathrm{obs}} \le \min\left\{ 4,\, 2+2\sum_{q\in Q}(1-Z_q) \right\}, \] so a flat rate above \[ \frac{5-\sqrt2}{4}\simeq0.896447 \] excludes every Bell-local measurement-independent selection model covered by this bound when \(S_{\mathrm{obs}}=2\sqrt2\).Finally, an exact eight-state reconstruction of a published post-processing model has acceptance rate \(3/4\) in every setting context while attaining the algebraic CHSH value \(4\). Its accepted laws satisfy \[ \Delta_Q=1, \qquad D_Q=\frac13, \] saturating both the selection-inflation lower bounds and the upper bounds permitted by the absolute rate. Thus rate flatness is not a certificate of fair sampling, although the absolute rate remains quantitatively useful. The quantity requiring structural certification is the conditional acceptance function, or a sufficient experimentally accessible proxy for it.