There seem to be some confusion about what I implied by position and responsibility so let me explain a bit more. I was refering to the situation where an admin is the final deciding vote for a demotion or internal issue. This does not mean supermods don't play a big part in the decision making process to handle complaints but simply put they are not the final decision makers. Since that decision on how to handle the situation is finalized by the admin it should be the admin's (or someone specifically assign to it) who is a primary means of communication.
Example:
Company hires someone and the first day they go to HR to get setup and shown around. They are there for a while and maybe one day someone complains about their quality of work. Now their manger has to go and review the complaint. The manager ends up deciding they want the person fired so they go to HR and say lets fire this person. Now HR has to setup the exit process for that person (removing them from computers, exit interview, getting back company property etc).
So now in that example HR is comparable to Admin's (Or a specifically assign entity to deal with this) which is the primary means of communication as well as the functional body behind the firing and the overall final decision makers.
Does this clear it up?
