Persistent memory supports personalized agents, but a stale stored fact can override current authoritative evidence without warning. We study when this harm begins as model capability changes. We evaluate a frozen, closed-set, action-scored benchmark with 2 suites that represent 2 different meanings of "no memory" (a Benefit suite, unsolvable without the stored fact, and a Safety suite, in which an authoritative tool always holds the correct value), on a same-family model-size series (Qwen3 0.6/1.7/4/8B). The Memory Trust Gap reflects over-trust rather than confusion. In the Benefit suite, models answer with the stale value 0.92-1.00 of the time at every scale. In the Safety suite, harm below the no-memory baseline under the trap conditions ($Δ_{\mathrm{mem}}$) is capability-gated, with the larger models collapsing most once a stale note is made to look current. In a $2\times2\times2\times2$ factorial, which feature triggers over-trust depends on both the feature and model scale. Removing a label amplifies over-trust at every size, and a recency feature (stale dated newer) fools the larger models harder. Source authority is weak and scale-flat, and position changes from positive to negative across the Qwen3 model-size series. We confirm these scale interactions with direct cross-size contrast tests rather than overlapping per-model intervals. Mitigation is likewise capability-dependent: exposing metadata improves accuracy for the capable models, but only pre-resolving the conflict restores accuracy for the 2 smaller checkpoints. The same pattern appears on the capable models in an independent Llama-Instruct model-size series and on 2 external datasets (RGB, MisBench). A framing control finds no consistent advantage for the memory label: at the 3 smaller scales, models trust a stale document more than a stale memory; at 8B, the difference is not significant.

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