No, in this case I think you're mistaken. "Rec" means whatever is the definition of the variable can reference the variable itself.
In other words, the default behaviour is that the scope, during variable definition, does not include the variable being defined. With "rec" the variable being defined is added to the scope in the definition of the variable itself.
Coming from lambda calculus, this makes sense: functions themselves cannot be recursive. What makes them recursive is taking their own definition as a parameter, I.e. getting their name in their scope.