The local reasoning in this situation is you putting the refuse in the bin and placing it outside. All of that is "pure", completely in your control, and relies on exactly no side effects or outside state. It's also trivially testable, nearly failure proof, and completely observable. The "locality" of this implies that you need only consider exactly the things which are "in scope" at this moment and their behavior is entirely circumscribed by your "local" scope.
The moment you rely on an outside party whose capabilities rely on outside state then you lose all of those guarantees.
From a certain, high-enough level we can have "local reasoning" again in that the state of the municipal recycling service is encompassed. Or perhaps we also need to include the world oil supply in that model, who knows?
So, I'm being pedantic around the word "local reasoning". I think that's valuable because the kind of reasoning which is local is sharply distinct from that which isn't and it confers a lot of great properties. Finally, I'll reiterate, that I think side effects of any form utterly wreck local reasoning.
