Preserving Every Target Row Does Not Preserve Propagated Uncertainty in Recursive Fitted Evaluation

Bootstrap procedures use ensembles of value functions to estimate uncertainty in a policy's value through recursive fitted evaluation. Fixing the target vectors leaves unspecified which model fits each vector, a choice implementations make implicitly. We show that reassigning those vectors among models can collapse ensemble spread by changing their dependence on the models' bootstrap resamples and fitting histories. We prove that reassigning target vectors can change the limiting distribution as ensemble size grows at fixed recursion depth and derive exact finite-ensemble moment recursions for affine fits. In Bootstrap-FQE experiments across six environments, reassignment at every update reduces spread on all 105 datasets and lowers observed coverage of nominal 90% intervals from 88–100% to 4–30% against the evaluation references. Indexing choices that determine which model fits each vector therefore belong to the ensemble's statistical specification.