How do learners acquire knowledge of what is unacceptable without negative evidence? Construction Grammar proposes statistical preemption: exposure to a conventional form (e.g., "donated the books to the library") preempts structurally possible but unattested alternatives ("*donated the library the books"). We present a computational study that, for the first time, directly dissociates statistical preemption from the competing entrenchment hypothesis in large language models within a single converging design. Across four experiments spanning 120 English verb-construction pairings (dative, causative, locative), we show that (1) LLM surprisal patterns correlate strongly with human acceptability judgments ($r = 0.79$), validated against three independent behavioral datasets; (2) these patterns are driven by competing-form frequency rather than overall verb frequency, confirmed by non-circular partial correlations; (3) preemption sensitivity scales as a power law with model size; and (4) a controlled fine-tuning intervention causally demonstrates that manipulating competing-form frequencies shifts preemption behavior in the predicted direction, with reverse-direction controls ruling out frequency-sensitivity confounds. These results provide converging evidence that neural language models acquire negative linguistic knowledge through distributional competition, the core mechanism posited by Construction Grammar.