Why can I access a derived private member function via a base class pointer to a derived object?

#include<iostream>

using namespace std;
class base
{
public:
    virtual void add() {
        cout << "hi";
    }
};

class derived : public base
{
private:
    void add() {
        cout << "bye";
    }
};

int main()
{
    base *ptr;
    ptr = new derived;
    ptr->add();
    return 0;
}

Output is bye

I dont have a problem with how this is implemented. I understand you use vtables and the vtable of derived contains the address of the new add() function. But add() is private shouldn't compiler generate an error when I try to access it outside the class? Somehow it doesn't seem right.