Video LLMs fail conspicuously at counting how many times an object crosses the screen, a failure attributed to missing object permanence. Using construction-grounded synthetic testbeds with validated labels, we show this attribution is incomplete: the count signal is present but unread - linear probes decode per-window presence at 93% while global count decoding collapses to a duration confound. Concurrent work reports the same representation-output dissociation for repetition counting; we show that in exit-and-reappear event counting it is repairable: two readout-directed repairs (episode-localization supervision and a discrete event-symbol side channel) raise same-object counting from 46.7% to 65.0% (oracle 66.7%) on a chance-33% benchmark across 7B-30B systems. Transfer to an independent factory costs nothing, and a measurement audit exposes five data-integrity failures that had obscured the boundary. A real-video audit (REALCOUNT, n=18, blind-audited) shows the boundary persists - best 55.6% at chance 33.3% - and symbol transfer fails zero-shot. A 1-epoch in-domain adaptation bench is negative (six levers at 28-50%), but 3 epochs reverse this for the symbol channel: with oracle timelines the reader reaches 94.4% sequence-disjoint (and 100% strict on the full set), while the deployed 2-epoch head reaches 61.1% in all three seeds (42-44), no better than a shuffled-symbol control (61.1% seed 42, 66.7% seed 43), and one clip above the unadapted reader (55.6%). The residual gap is detector evidence, not reader capacity: the same reader reaches 72.2-88.9% on GT timelines. The failure is repairable with informative timelines, but the deployed head remains the bottleneck; a frozen-feature boundary probe is weak (AUC 0.62 vs. 0.51 permutation) and non-transferring (0.77 within-clip vs. 0.62 across windows).

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