That is correct. That is very different, however, from saying "There are [effectively] no admins". That would be like saying "On a wiki, there are [effectively] no editors". That's just absurd.
It's just a difference in the definition of admin. Is an admin a person with access to what we call "admin tools", or is it a person with access to tools not available to everyone else? When we say we need admins to deal with major vandalism, we are using the 2nd definition. You are using the first.