Wireless network access

Hello.

I have a question related to wireless networks and routers. What I want to ask is if we can speak of a an acces to the router when the user navigates to the internet through the wireless network?
So...if the user access the configuration page of the router through the browser than we can say that the agent is "in the router", right? What if he does not access the router in that particular way, but connects to the wireless network (inserting a password) and than connects to the internet? Would this interaction of the user with the router would be equivalent to an access to the router? I understand that at first sight the user access only the wireless NETWORK and not the router, because he does not have access to the routers internal files or configuration just to the internet service. But, for the user to have access to the internet service he must interact with the routers functions (routing and forwarding), right? So if he can "access" those router functions, couldn't we say that the user has an access to the router itself?

I would like some clarification on this issue if you can help me with that.
Thanks a lot.