RAII has nothing to do with reference counting, it stands for resource acquisition is initialization. In C++ that means the lifetime of a resource is tied to the creation and destruction of an object. Often when people talk about RAII and C++ they are also referring to destructors being called when an object goes out of scope, so if an object that contains an object containing some allocated resource goes out of scope, the resource is released as the destructor path is called.
If an object with a smart pointer goes out of scope, then of course there's the overhead of the smart pointer, but the previous comment wasn't referring to that situation
RAII is commonly used for representing smart pointers that manage references to objects that themselves have otherwise pervasive lifetimes.
RAII not managing any shared resources is trivial and uninteresting. The lifecycle of an object that is confined to a single lexical scope can be handled manually and verified by visual inspection (though of course it is more reliable to automate that with RAII or macros, not to mention less verbose).
If an object with a smart pointer goes out of scope, then of course there's the overhead of the smart pointer, but the previous comment wasn't referring to that situation