Although an LLM chat is the starting point for many, there are many other use cases. We had people build domotics systems to control their house using natural language, vision based assistants for surveillance (e.g. send a notification describing what's happening instead of a classic "Movement detected") etc. and everything remains on your device / in your network.
That line means that you don't need to create an account and get an API key from a provider (i.e. "asking for permission") to run inference. The main advantage is precisely that local AI runs on your terms, including how data is handled, and provably so, unlike cloud APIs where there's still an element of trust with the operator.