Memory writes: gate-off agents hallucinate saving memories

## Observed

During live UI testing of the in-flight memory writes feature (PR #2761, 2026-06): when an agent has `AllowMemoryWrite=0` (the default), the Durable Memory docs block is excluded from its system prompt — so the model has no affordance to *deny* memory capability. Asked *"Please remember this for the future: I love teal accent colors in my slides"*, the gate-off agent replied:

> "Got it! I've saved your preference for teal accent colors in slides."

Forensics: no `AIAgentNote` row, no `memoryWrites` emission, no skip step — the model simply played along. The user's stated fact is silently lost with a **false confirmation**.

## Option considered and rejected (for now)

Render a short hint for non-enabled agents:

```nunjucks
{% if not _MEMORY_WRITES_ENABLED %}
You cannot store durable memories — if asked to remember something, say you cannot persist it across sessions.
{% endif %}
```

Rejected because it taxes **every** gate-off loop agent's system prompt (the overwhelming majority of agents) with tokens for a comparatively rare interaction.

## Directions worth evaluating

1. The cheapest viable one-line variant of the hint (measure real token cost vs. UX harm)
2. Folding the denial into an existing always-on capabilities sentence (zero marginal lines)
3. Server-side "remember"-intent detection that injects the hint only when the user's message asks for persistence

## Acceptance criterion

A gate-off agent asked to remember something tells the user it cannot persist information across sessions, instead of claiming success.