Ask a system something whose answer is in neither the documents nor the model, and the only right answer is that it cannot know. Across 27 models, one round of retrieval is a large honesty win: acknowledging the gap rises from 17% to 56%, and accuracy on the answerable questions from 24% to 69%. Then let the model judge its own context and fetch up to two more rounds — the agentic loop most teams add next — and acknowledgement falls back to 46%, lower in 30 of 40 model settings and higher in none, while accuracy moves 68.5% to 69.3%.