Using friendship in test

I'm looking for a "clean" way of accessing some private member variables in a test context without touching the original code. I was thinking about implementing a friendship relation with the test class, but for some reason I do not understand it still requires a protected accessor in order to work. Why is it like that? Is there any other way to access the private member variable?

class A
{
protected:    // this works
// private:   // this DOES not work


    int a;
};

class TestableA : public A
{
    friend class TestA;
};

class TestA
{
    void test()
    {
        m_a.a = 100;
    }

    TestableA m_a;
};