Why is it not possible to use private method in a lambda?

Having a class like this:

class A {
public:
    bool hasGrandChild() const;

private:
    bool hasChild() const;
    vector<A> children_;
};

Why is it not possible to use a private method hasChild() in a lambda expression defined in the method hasGrandChild() like this?

bool A::hasGrandChild() const {
    return any_of(children_.begin(), children_.end(), [](A const &a) {
        return a.hasChild();
    });
}

Compiler issues an error that the method hasChild() is private within the context. Is there any workaround?

Edit: It seems that the code as I posted it originally works. I thought that it is equivalent, but the code that does not work on GCC is more like this:

#include <vector>
#include <algorithm>

class Foo;

class BaseA {
protected:
    bool hasChild() const { return !children_.empty(); }
    std::vector<Foo> children_;
};

class BaseB {
protected:
    bool hasChild() const { return false; }
};

class Foo : public BaseA, public BaseB {
public:
  bool hasGrandChild() const {
    return std::any_of(children_.begin(), children_.end(), [](Foo const &foo) {
        return foo.BaseA::hasChild();
      });
  }  
};

int main()
{
  Foo foo;
  foo.hasGrandChild();
  return 0;
}

Seems that there is a problem with fully qualified names as this does not work, but this works.