As large language models (LLMs) are increasingly considered for automated assessment and feedback, understanding when LLM marking can be trusted is essential. We evaluate LLM-as-a-judge marking across three physics assessment formats - structured questions, written essays, and scientific plots - comparing GPT-5.2, Grok 4.1, Claude Opus 4.5, DeepSeek-V3.2, Gemini Pro 3, and committee aggregations against human markers under blind, solution-provided, false-solution, and exemplar-anchored conditions. For $n=771$ blind university exam questions, models achieve fractional mean absolute errors (fMAE) $\approx 0.22$ with robust discriminative validity (Spearman $ρ> 0.6$). For secondary and university structured questions ($n=1151$), providing official solutions reduces MAE and strengthens validity (committee $ρ= 0.88$); false solutions degrade absolute accuracy but leave rank ordering largely intact (committee $ρ= 0.77$; individual models $ρ\geq 0.59$). Essay marking behaves fundamentally differently. Across $n=55$ scripts ($n=275$ essays), blind AI marking is harsher and more variable than human marking, with discriminative validity already poor ($ρ\approx 0.1$). Adding a mark scheme does not improve discrimination ($ρ\approx 0$; all confidence intervals include zero). Anchored exemplars shift the AI mean close to the human mean and compress variance below the human standard deviation, but discriminative validity remains near-zero - distributional agreement can occur without valid discrimination. For code-based plot elements ($n=1400$), models achieve exceptionally high discriminative validity ($ρ> 0.84$) with near-linear calibration. Across all task types, validity tracks criterion-referenceability - the extent to which a task maps to explicit, observable grading features - and benchmark reliability, rather than raw model capability.