Action-conditioned world models are increasingly trained on data from randomized experiments, and whether their predictions respond to actions is usually checked by replacing or removing the actions and measuring the loss in accuracy. We show that such diagnostics report action effects where there are none: under autocorrelated designs, future actions stand in for history the model does not see, and a better model learns the stand-in better. When the design law is known, a conditional randomization test written as an e-value is valid in finite samples whatever the model, provided the resampler conditions on the full state the design used; resampling from a simpler law reproduces the false effect. We identify a second failure, specific to world models: when many sites share one action sequence (cells in a microscope field, pixels in a frame), the natural pooled score turns small model errors along the action contrast into overwhelming evidence against a true effect. In a pixel world, its median log e-value fell from $-17.3$ to $-6832$ as frames grew from 64 to 4096 pixels, while the oracle's rose. Tempering the score by a design effect estimated on training data changes the bet, not the validity. Our own preregistered analysis of optogenetic ERK experiments failed in exactly this way; a tempered statistic, selected on synthetic data and registered before the data were obtained, then rejected the null on a never-opened field ($E\approx 1.1\times10^{10}$). Every analysis is preregistered, fixed in a dated protocol before it was run, or labelled exploratory, and every reported result is generated from hashed result files.

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