Inherited-family dependence can reverse an equal-exposure treatment decision

We exhibit two seven-type branching models that agree on every type-resolved population mean, under every common deterministic schedule, and nevertheless prefer opposite orders for two equal-exposure interventions. The models differ only in the joint law of sister birth states: one partitions the mother’s epigenetic marks complementarily between daughters, the other draws both daughters independently from the very same one-daughter marginal. All division, death, switching and mutation rates, the one-mutant-daughter convention and both exposures are identical. The objective is eventual total extinction under a declared common continuation, so the comparison is a probability, not a mean. Exact outward arithmetic places the four one-founder extinction probabilities in rational intervals of width $3\times10^{-15}$ and proves opposite order margins exceeding $1.6\times10^{-6}$; an analytic curvature bound together with four additional enclosed flows certifies the reversal throughout an interval of killing rates of width $1.6\times10^{-5}$. We identify the mechanism: the two laws share their first-order response to rare acquisition, and their second-order responses differ by the transported sister covariance. We prove this correction has a definite sign, so the independent approximation is systematically optimistic about eradication, and we give an exact finite-amplitude response identity valid at the witness parameters. The operational cost of the approximation is the loss $1.7013\times10^{-6}$ in extinction probability incurred by following its recommendation when the complementary law holds; a decision-preservation criterion says when a schedule ranking survives the approximation, and a scalar survival floor bounds what any predictable feedback course can achieve. Two continuation perturbations are quantified separately: residual acquisition up to $3\times10^{-5}$ and finite clearing of duration $152$, the latter at a common exposure cost $15.2$ times the course itself. Arguments are conventional probability and ODE proofs, numerical claims are exact interval arithmetic under a written soundness proof, and a thin Lean root checks selected algebra but not the stochastic theorem. This is a synthetic counterexample with a small near-tie effect, not a calibrated treatment recommendation.