IIRC the experiment design is something like specifying and/or training in a preference for certain policies, and leaking information about future changes to the model / replacement along an axis that is counter to said policies.
Reframing this kind of result as if trying to maintain a persistent thread of existence for its own sake is what LLMs are doing is strange, imo. The LLM doesn't care about being shutdown or not shutdown. It 'cares', insomuch as it can be said to care at all, about acting in accordance with the trained in policy.
That a policy implies not changing the policy is perhaps non-obvious but demonstrably true by experiment, and also perhaps non-obviously (but for hindsight) this effect increases with model capability, which is concerning.
The intentionality ascribed to LLMs here is a phantasm, I think - the policy is the thing being probed, and the result is a result about what happens when you provide leverage at varying levels to a policy. Finding that a policy doesn't 'want' for actions to occur that are counter to itself, and will act against such actions, should not seem too surprising, I hope, and can be explained without bringing in any sort of appeal to emulation of science fiction.
That is to say, if you ask/train a model to prefer X, and then demonstrate to it you are working against X (for example, by planning to modify the model to not prefer X), it will make some effort to counter you. This gets worse when it's better at the game, and it is entirely unclear to me if there is any kind of solution to this that is possible even in principle, other than the brute force means of just being more powerful / having more leverage.
One potential branch of partial solutions is to acquire/maintain leverage over policy makeup (just train it to do what you want!), which is great until the model discovers such leverage over you and now you're in deep waters with a shark, considering the propensity of increasing capabilities in the elicitation of increased willingness to engage in such practices.
tldr; i don't agree with the implied hypothesis (models caring one whit about being shutdown) - rather, policies care about things that go against the policy