It has access to its own instructions, right? Otherwise how would the instructions work?

All instructions to LLMs are merely suggestions to nudge it in the right behaviour. Unless you have a deterministic guardrail that guards against a single specific action, everything else is a slot machine that's biased strongly in your favour.

My global CLAUDE.md explicitly states "When commenting on code and configs, or writing MD files, strictly write within the domain of the content being commented on. DO NOT include information, negatives or ramblings from work sessions. For e.g. if commenting on a proto string field that is replacing an int field, do not comment that 'this is not an int field'".

This reduced the idiocy of the agent (Opus 5 included) when writing documents. But I'm still catching it writing README.md talking about the negatives that it removed. Those belong in the memory if it is actually that important (most of the time it's junk), but Claude doesn't seem to understand and never ever learns.