Why isn't the const qualifier working on pointer members on const objects?

Question

I know this has been asked a lot, but the only answers I could find was when the const-ness was actually casted away using (int*) or similar. Why isn't the const qualifier working on pointer type member variables on const objects when no cast is involved?

#include <iostream>

class bar {
public:
    void doit()       { std::cout << "    bar::doit() non-const\n"; }
    void doit() const { std::cout << "    bar::doit() const\n"; }
};

class foo {
    bar* mybar1;
    bar mybar2;
public:
    foo() : mybar1(new bar) {}
    void doit() const {
        std::cout << "foo::doit() const\n";
        std::cout << "  calling mybar1->doit()\n";
        mybar1->doit();  // This calls bar::doit() instead of bar::doit() const
        std::cout << "  calling mybar2.doit()\n";
        mybar2.doit(); // This calls bar::doit() const correctly
    }
    // ... (proper copying elided for brevity)
};

int main(void)
{
    const foo foobar;  // NOTE: foobar is const
    foobar.doit();
}

The code above yields the following output (tested in gcc 4.5.2 and vc100):

foo::doit() const
  calling mybar1->doit()
    bar::doit() non-const         <-- Why ?
  calling mybar2.doit()
    bar::doit() const